Relevant bibliographies by topics / High order convergence

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'High order convergence'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "High order convergence"

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Vaarmann, Otu. "HIGH ORDER ITERATIVE METHODS FOR DECOMPOSITION‐COORDINATION PROBLEMS." Technological and Economic Development of Economy 12, no. 1 (March 31, 2006): 56–61. http://dx.doi.org/10.3846/13928619.2006.9637723.

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Many real‐life optimization problems are of the multiobjective type and highdimensional. Possibilities for solving large scale optimization problems on a computer network or multiprocessor computer using a multi‐level approach are studied. The paper treats numerical methods in which procedural and rounding errors are unavoidable, for example, those arising in mathematical modelling and simulation. For the solution of involving decomposition‐coordination problems some rapidly convergent interative methods are developed based on the classical cubically convergent method of tangent hyperbolas (Chebyshev‐Halley method) and the method of tangent parabolas (Euler‐Chebyshev method). A family of iterative methods having the convergence order equal to four is also considered. Convergence properties and computational aspects of the methods under consideration are examined. The problems of their global implementation and polyalgorithmic strategy are discussed as well.
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Albizuri, F. Xabier, Alicia d'Anjou, Manuel Graña, and J. Antonio Lozano. "Convergence Properties of High-order Boltzmann Machines." Neural Networks 9, no. 9 (December 1996): 1561–67. http://dx.doi.org/10.1016/s0893-6080(96)00026-3.

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Bokanowski, Olivier, Athena Picarelli, and Christoph Reisinger. "High-order filtered schemes for time-dependent second order HJB equations." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 1 (January 2018): 69–97. http://dx.doi.org/10.1051/m2an/2017039.

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In this paper, we present and analyse a class of “filtered” numerical schemes for second order Hamilton–Jacobi–Bellman (HJB) equations. Our approach follows the ideas recently introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the Monge-Ampère partial differential equation, SIAM J. Numer. Anal. 51 (2013) 423–444, and more recently applied by other authors to stationary or time-dependent first order Hamilton–Jacobi equations. For high order approximation schemes (where “high” stands for greater than one), the inevitable loss of monotonicity prevents the use of the classical theoretical results for convergence to viscosity solutions. The work introduces a suitable local modification of these schemes by “filtering” them with a monotone scheme, such that they can be proven convergent and still show an overall high order behaviour for smooth enough solutions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests from mathematical finance, focussing also on the use of backward differencing formulae for constructing the high order schemes.
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Hemker, Pieter W., Grigorii I. Shishkin, and Lidia P. Shishkina. "High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions." Computational Methods in Applied Mathematics 2, no. 1 (2002): 3–25. http://dx.doi.org/10.2478/cmam-2002-0001.

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AbstractThe boundary-value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. The order of convergence for the known ε-uniformly convergent schemes does not exceed 1. In this paper, using a defect correction technique, we construct ε-uniformly convergent schemes of highorder time-accuracy. The efficiency of the new defect-correction schemes is confirmed by numerical experiments. A new original technigue for experimental studying of convergence orders is developed for the cases where the orders of convergence in the x-direction and in the t-direction can be substantially different.
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Behl, Ramandeep, Ioannis K. Argyros, and Fouad Othman Mallawi. "Some High-Order Convergent Iterative Procedures for Nonlinear Systems with Local Convergence." Mathematics 9, no. 12 (June 14, 2021): 1375. http://dx.doi.org/10.3390/math9121375.

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In this study, we suggested the local convergence of three iterative schemes that works for systems of nonlinear equations. In earlier results, such as from Amiri et al. (see also the works by Behl et al., Argryos et al., Chicharro et al., Cordero et al., Geum et al., Guitiérrez, Sharma, Weerakoon and Fernando, Awadeh), authors have used hypotheses on high order derivatives not appearing on these iterative procedures. Therefore, these methods have a restricted area of applicability. The main difference of our study to earlier studies is that we adopt only the first order derivative in the convergence order (which only appears on the proposed iterative procedure). No work has been proposed on computable error distances and uniqueness in the aforementioned studies given on Rk. We also address these problems too. Moreover, by using Banach space, the applicability of iterative procedures is extended even further. We have examined the convergence criteria on several real life problems along with a counter problem that completes this study.
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Artidiello, Santiago, Alicia Cordero, Juan R. Torregrosa, and María P. Vassileva. "Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/289029.

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We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we show an extension to higher order, adding only one functional evaluation of the vectorial nonlinear function. We perform numerical tests to compare the proposed methods with other schemes in the literature and test their effectiveness on specific nonlinear problems. Moreover, some real basins of attraction are analyzed in order to check the relation between the order of convergence and the set of convergent starting points.
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Kiran, Quanita, and Tayyab Kamran. "Nadler’s type principle with high order of convergence." Nonlinear Analysis: Theory, Methods & Applications 69, no. 11 (December 2008): 4106–20. http://dx.doi.org/10.1016/j.na.2007.10.041.

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Wang, Wen Kai, and Huan Xin Peng. "High-Order Distributed Consensus with One-Bit Adaptive Quantization." Advanced Materials Research 591-593 (November 2012): 1299–302. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.1299.

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The convergence performance of distributed consensus algorithm with adaptive quantization communication depends on the convergence rate of the distributed consensus algorithm. In order to improve the convergence performance of distributed consensus under adaptive quantization communication, based on the one-bit adaptive quantization scheme, we propose the high-order distributed consensus to update the state of every node. We analyze the convergence performance and calculate the mean square error of the high-order distributed consensus algorithm with one-bit adaptive quantization. The high-order distributed consensus with one-bit adaptive quantization achieves a consensus in a mean square sense. Simultaneously, Simulations are done about the high-order distributed consensus based on one-bit adaptive quantization. Results show that the high-order distributed consensus algorithm based on one-bit adaptive quantization can reach an average consensus, and its convergence rate is higher than those of the first-order adaptive quantized distributed consensus algorithm and second-order adaptive quantized distributed consensus algorithm.
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Bin Jebreen, Haifa. "Constructing a High-Order Globally Convergent Iterative Method for Calculating the Matrix Sign Function." Mathematical Problems in Engineering 2018 (June 21, 2018): 1–9. http://dx.doi.org/10.1155/2018/8973867.

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This work is concerned with the construction of a new matrix iteration in the form of an iterative method which is globally convergent for finding the sign of a square matrix having no eigenvalues on the axis of imaginary. Toward this goal, a new method is built via an application of a new four-step nonlinear equation solver on a particulate matrix equation. It is discussed that the proposed scheme has global convergence with eighth order of convergence. To illustrate the effectiveness of the theoretical results, several computational experiments are worked out.
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Proinov, Petko D., and Maria T. Vasileva. "A New Family of High-Order Ehrlich-Type Iterative Methods." Mathematics 9, no. 16 (August 5, 2021): 1855. http://dx.doi.org/10.3390/math9161855.

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One of the famous third-order iterative methods for finding simultaneously all the zeros of a polynomial was introduced by Ehrlich in 1967. In this paper, we construct a new family of high-order iterative methods as a combination of Ehrlich’s iteration function and an arbitrary iteration function. We call these methods Ehrlich’s methods with correction. The paper provides a detailed local convergence analysis of presented iterative methods for a large class of iteration functions. As a consequence, we obtain two types of local convergence theorems as well as semilocal convergence theorems (with computer verifiable initial condition). As special cases of the main results, we study the convergence of several particular iterative methods. The paper ends with some experiments that show the applicability of our semilocal convergence theorems.
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Dissertations / Theses on the topic "High order convergence"

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Hao, Zhaopeng. "High-order numerical methods for integral fractional Laplacian: algorithm and analysis." Digital WPI, 2020. https://digitalcommons.wpi.edu/etd-dissertations/612.

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The fractional Laplacian is a promising mathematical tool due to its ability to capture the anomalous diffusion and model the complex physical phenomenon with long-range interaction, such as fractional quantum mechanics, image processing, jump process, etc. One of the important applications of fractional Laplacian is a turbulence intermittency model of fractional Navier-Stokes equation which is derived from Boltzmann's theory. However, the efficient computation of this model on bounded domains is challenging as highly accurate and efficient numerical methods are not yet available. The bottleneck for efficient computation lies in the low accuracy and high computational cost of discretizing the fractional Laplacian operator. Although many state-of-the-art numerical methods have been proposed and some progress has been made for the existing numerical methods to achieve quasi-optimal complexity, some issues are still fully unresolved: i) Due to nonlocal nature of the fractional Laplacian, the implementation of the algorithm is still complicated and the computational cost for preparation of algorithms is still high, e.g., as pointed out by Acosta et al \cite{AcostaBB17} 'Over 99\% of the CPU time is devoted to assembly routine' for finite element method; ii) Due to the intrinsic singularity of the fractional Laplacian, the convergence orders in the literature are still unsatisfactory for many applications including turbulence intermittency simulations. To reduce the complexity and computational cost, we consider two numerical methods, finite difference and spectral method with quasi-linear complexity, which are summarized as follows. We develop spectral Galerkin methods to accurately solve the fractional advection-diffusion-reaction equations and apply the method to fractional Navier-Stokes equations. In spectral methods on a ball, the evaluation of fractional Laplacian operator can be straightforward thanks to the pseudo-eigen relation. For general smooth computational domains, we propose the use of spectral methods enriched by singular functions which characterize the inherent boundary singularity of the fractional Laplacian. We develop a simple and easy-to-implement fractional centered difference approximation to the fractional Laplacian on a uniform mesh using generating functions. The weights or coefficients of the fractional centered formula can be readily computed using the fast Fourier transform. Together with singularity subtraction, we propose high-order finite difference methods without any graded mesh. With the use of the presented results, it may be possible to solve fractional Navier-Stokes equations, fractional quantum Schrodinger equations, and stochastic fractional equations with high accuracy. All numerical simulations will be accompanied by stability and convergence analysis.
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Sayi, Mbani T. "High Accuracy Fitted Operator Methods for Solving Interior Layer Problems." University of the Western Cape, 2020. http://hdl.handle.net/11394/7320.

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Philosophiae Doctor - PhD
Fitted operator finite difference methods (FOFDMs) for singularly perturbed problems have been explored for the last three decades. The construction of these numerical schemes is based on introducing a fitting factor along with the diffusion coefficient or by using principles of the non-standard finite difference methods. The FOFDMs based on the latter idea, are easy to construct and they are extendible to solve partial differential equations (PDEs) and their systems. Noting this flexible feature of the FOFDMs, this thesis deals with extension of these methods to solve interior layer problems, something that was still outstanding. The idea is then extended to solve singularly perturbed time-dependent PDEs whose solutions possess interior layers. The second aspect of this work is to improve accuracy of these approximation methods via methods like Richardson extrapolation. Having met these three objectives, we then extended our approach to solve singularly perturbed two-point boundary value problems with variable diffusion coefficients and analogous time-dependent PDEs. Careful analyses followed by extensive numerical simulations supporting theoretical findings are presented where necessary.
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Davis, Clayton Paul. "Understanding and Improving Moment Method Scattering Solutions." Diss., CLICK HERE for online access, 2004. http://contentdm.lib.byu.edu/ETD/image/etd620.pdf.

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Vergnaud, Alban. "Améliorations de la précision et de la modélisation de la tension de surface au sein de la méthode SPH, et simulations de cas d'amerrissage d'urgence d'helicoptères." Thesis, Ecole centrale de Nantes, 2020. http://www.theses.fr/2020ECDN0033.

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La méthode SPH (Smoothed Particle Hydrodynamics) est une méthode de simulation numérique Lagrangienne et sans maillage, utilisée dans de nombreux domaines de la physique et de l’ingénierie (astrophysique, mécanique des milieux solides, mécanique des milieux fluides, etc...). Dans le domaine de la mécanique des fluides, cette méthode est désormais utilisée dans de nombreux champs d’application (ingénierie navale, automobile, aéronautique, etc...), profitant en particulier de son caractère Lagrangien et de l'absence de connectivités pour simuler des écoulements complexes à surface libre avec de grandes déformations et de nombreuses reconnexions d’interfaces. Cependant, la méthode SPH souffre encore d’un certain manque de précision dû à son caractère Lagrangien et à la relative complexité des opérateurs utilisés. L’objectif général de cette thèse est de proposer plusieurs améliorations en vue d’augmenter la précision de la méthode SPH. Le premier axe de ce travail de recherche porte sur l’étude du désordre particulaire (ou "particle shifting" en anglais) afin de briser les structures Lagrangiennes classiquement observées en SPH et responsables d'une dégradation de la précision des simulations. En particulier, à l’aide d’une étude théorique portant notamment sur des propriétés de convergence et de consistance, une nouvelle loi de shifting est proposée. Un deuxième axe s'intéresse à l'étude d'un nouvel opérateur visqueux en proche paroi, pour un traitement surfacique des conditions aux limites. Le troisième axe de développement concerne la montée en ordre de la méthode SPH, et notamment dans le cas des schémas de type Riemann-SPH. Une nouvelle méthode de reconstruction, basée sur le schéma WENO (Weighted Essentially Non-Oscillatory) et des interpolations MLS (Moving Least Squares), des états gauche et droit des problèmes de Riemann est proposée. En complément de ces recherches, un nouveau modèle de tension de surface précis et robuste est proposé pour les écoulements monophasiques, permettant notamment une imposition de l’angle de contact au niveau de la ligne de contact. Enfin, dans le cadre du projet SARAH (increased SAfety and Robust certification for ditching of Aircraft and Helicopters ; European Unions Horizon 2020 Research and Innovation Programme Grant No. 724139), le dernier axe de cette thèse est consacré à la mise en place d’un modèle numérique permettant la simulation de cas d’amerrissage d’urgence d’hélicoptère. Ce modèle est validé grâce à la comparaison des résultats numériques avec ceux obtenus lors d’une campagne d’essais expérimentaux menée au bassin d'essais de l'Ecole Centrale de Nantes
Smoothed Particle Hydrodynamics (SPH) is a Lagrangian and meshless numerical method, used in many branches of physics and engineering (astrophysics, solid mechanics, fluid mechanics, etc...). In fluid mechanics, this method is now used in many application fields (naval engineering, automotive engineering, aeronautic engineering, etc...), using its meshless and Lagrangian features to simulate free surface flows with complex shapes and with many interface reconnexions. However, the SPH method still suffers from a lack of precision due to its Lagrangian feature and the relative complexity of the SPH operators. The objective of this thesis is to propose several improvements to increase the precision of the SPH method. The first part of this work focuses on a particle shifting technique aiming at breaking the Lagrangian structures inherently observed in SPH and which usually leads to a deterioration of the simulations. In particular, thanks to a theoretical study on consistency and convergence properties, a new shifting law is proposed. Secondly, a new viscous operator for near-body areas is proposed, based on a surface formulation of the boundary conditions. The third part concerns higher orders of convergence in the SPH method, and in particular for the case of Riemann-SPH schemes. A new reconstruction method, based the WENO scheme (Weighted Essentially Non-Oscillatory) and MLS (Moving Least Squares) interpolations, is proposed for the left and right state reconstructions of the Riemann problems. Then, a new accurate and robust surface tension model for single-phase flows is proposed, allowing namely to impose the contact angles at the contact line. Finally, as part of the SARAH project (increased SAfety and Robust certification for ditching of Aircraft and Helicopters ; European Unions Horizon 2020 Research and Innovation Programme Grant No. 724139), the last topic of this thesis is dedicated to the establishment of a numerical model allowing the SPH simulations of emergency ditching cases of helicopters. This model is validated thanks to comparisons with experimental results conducted in the wave basin of Ecole Centrale Nantes
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Miller, Kenyon Russell. "Convergent neural algorithms for pattern matching using high-order relational descriptions." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/8219.

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Durochat, Clément. "Méthode de type Galerkin discontinu en maillages multi-éléments (et non-conformes) pour la résolution numérique des équations de Maxwell instationnaires." Thesis, Nice, 2013. http://www.theses.fr/2013NICE4005.

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Cette thèse porte sur l’étude d’une méthode de type Galerkin discontinu en domaine temporel (GDDT), afin de résoudre numériquement les équations de Maxwell instationnaires sur des maillages hybrides tétraédriques/hexaédriques en 3D (triangulaires/quadrangulaires en 2D) et non-conformes, que l’on note méthode GDDT-PpQk. Comme dans différents travaux déjà réalisés sur plusieurs méthodes hybrides (par exemple des combinaisons entre des méthodes Volumes Finis et Différences Finies, Éléments Finis et Différences Finies, etc.), notre objectif principal est de mailler des objets ayant une géométrie complexe à l’aide de tétraèdres, pour obtenir une précision optimale, et de mailler le reste du domaine (le vide environnant) à l’aide d’hexaèdres impliquant un gain en terme de mémoire et de temps de calcul. Dans la méthode GDDT considérée, nous utilisons des schémas de discrétisation spatiale basés sur une interpolation polynomiale nodale, d’ordre arbitraire, pour approximer le champ électromagnétique. Nous utilisons un flux centré pour approcher les intégrales de surface et un schéma d’intégration en temps de type saute-mouton d’ordre deux ou d’ordre quatre. Après avoir introduit le contexte historique et physique des équations de Maxwell, nous présentons les étapes détaillées de la méthode GDDT-PpQk. Nous réalisons ensuite une analyse de stabilité L2 théorique, en montrant que cette méthode conserve une énergie discrète et en exhibant une condition suffisante de stabilité de type CFL sur le pas de temps, ainsi que l’analyse de convergence en h (théorique également), conduisant à un estimateur d’erreur a-priori. Ensuite, nous menons une étude numérique complète en 2D (ondes TMz), pour différents cas tests, des maillages hybrides et non-conformes, et pour des milieux de propagation homogènes ou hétérogènes. Nous faisons enfin de même pour la mise en oeuvre en 3D, avec des simulations réalistes, comme par exemple la propagation d’une onde électromagnétique dans un modèle hétérogène de tête humaine. Nous montrons alors la cohérence entre les résultats mathématiques et numériques de cette méthode GDDT-PpQk, ainsi que ses apports en termes de précision et de temps de calcul
This thesis is concerned with the study of a Discontinuous Galerkin Time-Domain method (DGTD), for the numerical resolution of the unsteady Maxwell equations on hybrid tetrahedral/hexahedral in 3D (triangular/quadrangular in 2D) and non-conforming meshes, denoted by DGTD-PpQk method. Like in several studies on various hybrid time domain methods (such as a combination of Finite Volume with Finite Difference methods, or Finite Element with Finite Difference, etc.), our general objective is to mesh objects with complex geometry by tetrahedra for high precision and mesh the surrounding space by square elements for simplicity and speed. In the discretization scheme of the DGTD method considered here, the electromagnetic field components are approximated by a high order nodal polynomial, using a centered approximation for the surface integrals. Time integration of the associated semi-discrete equations is achieved by a second or fourth order Leap-Frog scheme. After introducing the historical and physical context of Maxwell equations, we present the details of the DGTD-PpQk method. We prove the L2 stability of this method by establishing the conservation of a discrete analog of the electromagnetic energy and a sufficient CFL-like stability condition is exhibited. The theoritical convergence of the scheme is also studied, this leads to a-priori error estimate that takes into account the hybrid nature of the mesh. Afterward, we perform a complete numerical study in 2D (TMz waves), for several test problems, on hybrid and non-conforming meshes, and for homogeneous or heterogeneous media. We do the same for the 3D implementation, with more realistic simulations, for example the propagation in a heterogeneous human head model. We show the consistency between the mathematical and numerical results of this DGTD-PpQk method, and its contribution in terms of accuracy and CPU time
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Sciannandrone, Daniele. "Acceleration and higher order schemes of a characteristic solver for the solution of the neutron transport equation in 3D axial geometries." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112171/document.

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Le sujet de ce travail de thèse est l’application de la méthode de caractéristiques longues (MOC) pour résoudre l’équation du transport des neutrons pour des géométries à trois dimensions extrudées. Les avantages du MOC sont sa précision et son adaptabilité, le point faible était la quantité de ressources de calcul requises. Ce problème est même plus important pour des géométries à trois dimensions ou le nombre d’inconnues du problème est de l’ordre de la centaine de millions pour des calculs d’assemblage.La première partie de la recherche a été dédiée au développement des techniques optimisées pour le traçage et la reconstruction à-la-volé des trajectoires. Ces méthodes profitent des régularités des géométries extrudées et ont permis une forte réduction de l’empreinte mémoire et une réduction des temps de calcul. La convergence du schéma itératif a été accélérée par un opérateur de transport dégradé (DPN) qui est utilisé pour initialiser les inconnues de l’algorithme itératif and pour la solution du problème synthétique au cours des itérations MOC. Les algorithmes pour la construction et la solution des opérateurs MOC et DPN ont été accélérés en utilisant des méthodes de parallélisation à mémoire partagée qui sont le plus adaptés pour des machines de bureau et pour des clusters de calcul. Une partie importante de cette recherche a été dédiée à l’implémentation des méthodes d’équilibrage la charge pour améliorer l’efficacité du parallélisme. La convergence des formules de quadrature pour des cas 3D extrudé a aussi été explorée. Certaines formules profitent de couts négligeables du traitement des directions azimutales et de la direction verticale pour accélérer l’algorithme. La validation de l’algorithme du MOC a été faite par des comparaisons avec une solution de référence calculée par un solveur Monte Carlo avec traitement continu de l’énergie. Pour cette comparaison on propose un couplage entre le MOC et la méthode des Sous-Groupes pour prendre en compte les effets des résonances des sections efficaces. Le calcul complet d’un assemblage de réacteur rapide avec interface fertile/fissile nécessite 2 heures d’exécution avec des erreurs de quelque pcm par rapport à la solution de référence.On propose aussi une approximation d’ordre supérieur du MOC basée sur une expansion axiale polynomiale du flux dans chaque maille. Cette méthode permet une réduction du nombre de mailles (et d’inconnues) tout en gardant la même précision.Toutes les méthodes développées dans ce travail de thèse ont été implémentées dans la version APOLLO3 du solveur de transport TDT
The topic of our research is the application of the Method of Long Characteristics (MOC) to solve the Neutron Transport Equation in three-dimensional axial geometries. The strength of the MOC is in its precision and versatility. As a drawback, it requires a large amount of computational resources. This problem is even more severe in three-dimensional geometries, for which unknowns reach the order of tens of billions for assembly-level calculations.The first part of the research has dealt with the development of optimized tracking and reconstruction techniques which take advantage of the regularities of three-dimensional axial geometries. These methods have allowed a strong reduction of the memory requirements and a reduction of the execution time of the MOC calculation.The convergence of the iterative scheme has been accelerated with a lower-order transport operator (DPN) which is used for the initialization of the solution and for solving the synthetic problem during MOC iterations.The algorithms for the construction and solution of the MOC and DPN operators have been accelerated by using shared-memory parallel paradigms which are more suitable for standard desktop working stations. An important part of this research has been devoted to the implementation of scheduling techniques to improve the parallel efficiency.The convergence of the angular quadrature formula for three-dimensional cases is also studied. Some of these formulas take advantage of the reduced computational costs of the treatment of planar directions and the vertical direction to speed up the algorithm.The verification of the MOC solver has been done by comparing results with continuous-in-energy Monte Carlo calculations. For this purpose a coupling of the 3D MOC solver with the Subgroup method is proposed to take into account the effects of cross sections resonances. The full calculation of a FBR assembly requires about 2 hours of execution time with differences of few PCM with respect to the reference results.We also propose a higher order scheme of the MOC solver based on an axial polynomial expansion of the unknown within each mesh. This method allows the reduction of the meshes (and unknowns) by keeping the same precision.All the methods developed in this thesis have been implemented in the APOLLO3 version of the neutron transport solver TDT
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Lin, Cheng-Bin, and 林誠斌. "Improvement On The Convergence Of High-Order QAM Blind Equalizer." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/09941380993125421762.

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碩士
國立海洋大學
電機工程學系
84
blind equalization techniques are of great interest in digital communication system in which the transmission of a training sequence is impractical or very costly. It has applicationin in multipoint networks systems, and in digital microwaveradio communication over multipath fading channels. Most conventional blind equalization techniques suffer from slow convergence rate,especially when high level modulations are use. In this thesis, we propose two aspects to improve the convergence properties of blind equalization. One is to modify the error function of the LMS-type blind equalization algorithm to speed up the convergence rate. In this regard, we introduce the stop-and-go dual-mode algorithms which can significantly improve the convergence properties of dual-mode type algorithms by simply adding a stop-and-go adaptation rule. The other is to use faster algorithms instead of the conventional LMS-type algorithms for blind equalization. In this regard, we introduce frequency-domain approximate RLS algorithm which exhibits an RLS-type convergence behavior while having the same order of magnitude of computational complexity as the LMS- type algorithm's. The proposed blind equalization techniques are compared with other blind equalization techniques in terms of the achieved convergence rate and error rate. The results indicate that the propose techniques outperform the conventional ones in both aspects. The goodness of the proposed techniques is demonstrated with the aid of computer simulations of 64-QAM over a telephone channel and 4-QAM over a multipath fading channel.
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Mehmetoglu, Orhan. "Stability and Convergence of High Order Numerical Methods for Nonlinear Hyperbolic Conservation Laws." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-08-11653.

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Recently there have been numerous advances in the development of numerical algorithms to solve conservation laws. Even though the analytical theory (existence-uniqueness) is complete in the case of scalar conservation laws, there are many numerically robust methods for which the question of convergence and error estimates are still open. Usually high order schemes are constructed to be Total Variation Diminishing (TVD) which only guarantees convergence of such schemes to a weak solution. The standard approach in proving convergence to the entropy solution is to try to establish cell entropy inequalities. However, this typically requires additional non-homogeneous limitations on the numerical method, which reduces the modified scheme to first order when the mesh is refined. There are only a few results on the convergence which do not impose such limitations and all of them assume some smoothness on the initial data in addition to L^infinity bound. The Nessyahu-Tadmor (NT) scheme is a typical example of a high order scheme. It is a simple yet robust second order non-oscillatory scheme, which relies on a non-linear piecewise linear reconstruction. A standard reconstruction choice is based on the so-called minmod limiter which gives a maximum principle for the scheme. Unfortunately, this limiter reduces the reconstruction to first order at local extrema. Numerical evidence suggests that this limitation is not necessary. By using MAPR-like limiters, one can allow local nonlinear reconstructions which do not reduce to first order at local extrema. However, use of such limiters requires a new approach when trying to prove a maximum principle for the scheme. It is also well known that the NT scheme does not satisfy the so-called strict cell entropy inequalities, which is the main difficulty in proving convergence to the entropy solution. In this work, the NT scheme with MAPR-like limiters is considered. A maximum principle result for a conservation law with any Lipschitz flux and also with any k-monotone flux is proven. Using this result it is also proven that in the case of strictly convex flux, the NT scheme with a properly selected MAPR-like limiter satisfies an one-sided Lipschitz stability estimate. As a result, convergence to the unique entropy solution when the initial data satisfies the so-called one-sided Lipschitz condition is obtained. Finally, compensated compactness arguments are employed to prove that for any bounded initial data, the NT scheme based on a MAPR-like limiter converges strongly on compact sets to the unique entropy solution of the conservation law with a strictly convex flux.
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Liang, Wen-Hsuan, and 梁文軒. "Design and Implementation of Fast Convergence Blind Equalizer for High-Order QAM Systems." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/17922717194976245683.

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碩士
中興大學
電機工程學系所
95
An efficient blind equalization with the two-stage single/multilevel modulus and decision-directed (DD) algorithm is proposed for high-order QAM (64/256/1024QAM) systems. The proposed blind equalization algorithm applies the two-stage convergence scheme, which derives from the modified constant modulus algorithm (MCMA) and the DD algorithm. We successfully test the proposed blind equalization algorithm with the cable channel model for 64/256/1024QAM modulations and with the ATTC channel model for 64QAM modulation. In the first convergence stage, the mixed MCMA and DD equalization is applied for fast convergence. When the convergence process reaches to the acceptable steady state, the convergence detector will transform the equalization process into the second stage. In the second convergence stage, the MCMA with multiple modulus, called the generalized MCMA （GMCMA）method and DD algorithms are applied for further reducing the mean square error (MSE) of equalizations. In 64/256/1024QAM modulations, the proposed method performs faster convergence speed than the previous well-know blind equalization methods. By adding convergence detector, the equalizer will increase extra hardware costs. But when the switching mode is active at the right time, the equalizer will achieve better converged performance, compared with the other algorithms. Simultaneously, the proposed algorithm also provides better MSE performance and the minimum symbol error rate (SER) than the other methods at the same SNR. Finally, we implement the blind equalization on the MATLAB and SimulinkTM environment and do the FPGA emulation on the SignalWAVeTM DSP+FPGA board.
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Books on the topic "High order convergence"

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Lewis Research Center. Institute for Computational Mechanics in Propulsion., ed. On high-order radiation boundary conditions. [Cleveland, Ohio]: National Aeronautics and Space Administration, Institute for Computational Mechanics in Propulsion, Langley Research Center, 1995.

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Lewis Research Center. Institute for Computational Mechanics in Propulsion., ed. On high-order radiation boundary conditions. [Cleveland, Ohio]: National Aeronautics and Space Administration, Institute for Computational Mechanics in Propulsion, Langley Research Center, 1995.

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On high-order radiation boundary conditions. [Cleveland, Ohio]: National Aeronautics and Space Administration, Institute for Computational Mechanics in Propulsion, Langley Research Center, 1995.

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Book chapters on the topic "High order convergence"

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Armenta, Roberto B., and Costas D. Sarris. "Boundary Modeling and High-Order Convergence in Finite-Difference Methods." In Computational Electromagnetics—Retrospective and Outlook, 225–43. Singapore: Springer Singapore, 2014. http://dx.doi.org/10.1007/978-981-287-095-7_9.

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Seitz, Timo, Ansgar Lechtenberg, and Peter Gerlinger. "Rocket Combustion Chamber Simulations Using High-Order Methods." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 381–94. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53847-7_24.

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Abstract High-order spatial discretizations significantly improve the accuracy of flow simulations. In this work, a multi-dimensional limiting process with low diffusion (MLP$$^\text {ld}$$) and up to fifth order accuracy is employed. The advantage of MLP is that all surrounding volumes of a specific volume may be used to obtain cell interface values. This prevents oscillations at oblique discontinuities and improves convergence. This numerical scheme is utilized to investigate three different rocket combustors, namely a seven injector methane/oxygen combustion chamber, the widely simulated PennState preburner combustor and a single injector chamber called BKC, where pressure oscillations are important.
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Liou, Meng-Sing, and Angelo Scandaliato. "Implicit High-Order Compact Differencing Methods: Study of Convergence and Stability." In Computational Fluid Dynamics 2008, 391–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01273-0_49.

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Argyros, I. K., M. I. Argyros, Á. A. Magreíñn, J. A. Sicilia, and Í. Sarría. "Convergence of Some High-Order Iterative Methods with Applications to Differential Equations." In Advanced Numerical Methods for Differential Equations, 187–204. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003097938-8.

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Guo, Zirong, Deyuan Meng, and Jingyao Zhang. "Robust Convergence of High-Order Adaptive Iterative Learning Control Against Iteration-Varying Uncertainties." In Lecture Notes in Electrical Engineering, 591–98. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9682-4_62.

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Cordero, Alicia, Juan R. Torregrosa, and María P. Vassileva. "New Family of Iterative Methods with High Order of Convergence for Solving Nonlinear Systems." In Lecture Notes in Computer Science, 222–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41515-9_23.

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Ditkowski, A. "High Order Finite Difference Schemes for the Heat Equation Whose Convergence Rates are Higher Than Their Truncation Errors." In Lecture Notes in Computational Science and Engineering, 167–78. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19800-2_13.

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Sartori, Nicolò. "EU–Turkey Energy Dialogue: Moving Beyond the Accession Negotiations Framework." In EU-Turkey Relations, 373–93. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70890-0_15.

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AbstractEnergy has long been perceived as a policy field where mutual strategic interests could lead to progressive policy convergence and enhanced cooperation between the EU and Turkey. This chapter evaluates the evolution of energy relations between the EU and Turkey, starting from early 2000s, paying specific attention to the key energy policies and the main bilateral dynamics in place in the energy domain. It analyzes the energy profiles and interests of Brussels and Ankara in order to evaluate whether or not the EU and Turkey have adopted mutually beneficial initiatives that foster convergence between the parties. Despite Ankara’s attempt to link energy cooperation primarily to the accession negotiations process, the EU has been able to keep the two tracks separated through the launch of parallel institutional initiatives which led to progressive policy alignment as long as the bilateral political conditions allowed it to maintain a structured dialogue. In recent years, the stalemate in accession negotiations and the rising tensions in the Eastern Mediterranean brought EU–Turkey energy dialogue to its historical low. Bottom-up technical and regulatory collaboration represents the most effective way to progress in bilateral energy cooperation, by decoupling energy dialogue from the formal accession negotiation process and underplaying the effects of high level political conflicts.
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Brayanov, Iliya, and Ivanka Dimitrova. "Uniformly Convergent High-Order Schemes for a 2D Elliptic Reaction-Diffusion Problem with Anisotropic Coefficients." In Numerical Methods and Applications, 395–402. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-36487-0_44.

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Akulenko, Leonid. "The Method of Accelerated Convergence for Eigenvalue Problems for Fourth-Order Equations." In High-Precision Methods in Eigenvalue Problems and Their Applications, 109–20. Chapman and Hall/CRC, 2004. http://dx.doi.org/10.1201/9780203401286.ch7.

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Conference papers on the topic "High order convergence"

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Chipman, Russell A., and Ravinderkumar Kinnera. "High-order PMD emulator." In ITCom 2001: International Symposium on the Convergence of IT and Communications, edited by Achyut K. Dutta, Abdul Ahad S. Awwal, Niloy K. Dutta, and Katsunari Okamoto. SPIE, 2001. http://dx.doi.org/10.1117/12.436015.

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Ostapenko, V., Michail D. Todorov, and Christo I. Christov. "On Convergence of High Order Shock Capturing Difference Schemes." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: Proceedings of the 2nd International Conference. AIP, 2010. http://dx.doi.org/10.1063/1.3526641.

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Liu, Jia. "High-Order Momentum: Improving Latency and Convergence for Wireless Network Optimization." In IEEE INFOCOM 2018 - IEEE Conference on Computer Communications. IEEE, 2018. http://dx.doi.org/10.1109/infocom.2018.8486254.

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Al-Ani, Mustafa, Andrzej Tarczynski Tarczynski, and Bashar I. Ahmad. "High-Order Hybrid Stratified Sampling: Fast Uniform-Convergence Fourier Transform Estimation." In 2018 52nd Asilomar Conference on Signals, Systems, and Computers. IEEE, 2018. http://dx.doi.org/10.1109/acssc.2018.8645361.

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Choi, Jihee, and Hong Jeong. "Defect Extraction in Photomask Image Using High Order Moment." In 2009 Fourth International Conference on Computer Sciences and Convergence Information Technology. IEEE, 2009. http://dx.doi.org/10.1109/iccit.2009.175.

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Magreñán, Á. A., I. K. Argyros, Í. Sarría, and J. A. Sicilia. "Local convergence and the dynamics of a family of high convergence order method for solving nonlinear equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043940.

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Japikse, David, Oleg Dubitsky, Kerry N. Oliphant, Robert J. Pelton, Daniel Maynes, and Jamin Bitter. "Multi-Variable, High Order, Performance Models (2005C)." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79416.

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In the course of developing advanced data processing and advanced performance models, as presented in companion papers, a number of basic scientific and mathematical questions arose. This paper deals with questions such as uniqueness, convergence, statistical accuracy, training, and evaluation methodologies. The process of bringing together large data sets and utilizing them, with outside data supplementation, is considered in detail. After these questions are focused carefully, emphasis is placed on how the new models, based on highly refined data processing, can best be used in the design world. The impact of this work on designs of the future is discussed. It is expected that this methodology will assist designers to move beyond contemporary design practices.
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Iacono, Francesca, and Georg May. "Convergence Acceleration for Simulation of Steady-State Compressible Flows Using High-Order Schemes." In 19th AIAA Computational Fluid Dynamics. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-4132.

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Li, Lei. "High-order PDα-type iterative learning control and its Lebesgue-p norm convergence." In 2017 IEEE 6th Data Driven Control and Learning Systems Conference (DDCLS). IEEE, 2017. http://dx.doi.org/10.1109/ddcls.2017.8068136.

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Quandt, Martin, Claus-Dieter Munz, and Rudolf Schneider. "Convergence, stability and accuracy of a new high order relativistic particle push method." In 2008 IEEE 35th International Conference on Plasma Science (ICOPS). IEEE, 2008. http://dx.doi.org/10.1109/plasma.2008.4591158.

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Reports on the topic "High order convergence"

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Qiu, Jing-Mei, and Chi-Wang Shu. Convergence of High Order Finite Volume Weighted Essentially Non-Oscillatory Scheme and Discontinuous Galerkin Method for Nonconvex Conservation Laws. Fort Belvoir, VA: Defense Technical Information Center, January 2007. http://dx.doi.org/10.21236/ada468107.

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