Relevant bibliographies by topics / Asymptotic Iteration Method

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Asymptotic Iteration Method'

Author: Grafiati
Published: 4 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Asymptotic Iteration Method"

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Ismail, Mourad E. H., and Nasser Saad. "The asymptotic iteration method revisited." Journal of Mathematical Physics 61, no. 3 (2020): 033501. http://dx.doi.org/10.1063/1.5117143.

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CHAMPION, BRODIE, RICHARD L. HALL, and NASSER SAAD. "ASYMPTOTIC ITERATION METHOD FOR SINGULAR POTENTIALS." International Journal of Modern Physics A 23, no. 09 (2008): 1405–15. http://dx.doi.org/10.1142/s0217751x08039852.

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The asymptotic iteration method (AIM) is applied to obtain highly accurate eigenvalues of the radial Schrödinger equation with the singular potential V(r) = r2+λ/rα(α,λ>0) in arbitrary dimensions. Certain fundamental conditions for the application of AIM, such as a suitable asymptotic form for the wave function, and the termination condition for the iteration process, are discussed. Several suggestions are introduced to improve the rate of convergence and to stabilize the computation. AIM offers a simple, accurate, and efficient method for the treatment of singular potentials, such as V(r),
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Ciftci, Hakan, Richard L. Hall, and Nasser Saad. "Asymptotic iteration method for eigenvalue problems." Journal of Physics A: Mathematical and General 36, no. 47 (2003): 11807–16. http://dx.doi.org/10.1088/0305-4470/36/47/008.

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YEE, H. C., and P. K. SWEBY. "GLOBAL ASYMPTOTIC BEHAVIOR OF ITERATIVE IMPLICIT SCHEMES." International Journal of Bifurcation and Chaos 04, no. 06 (1994): 1579–611. http://dx.doi.org/10.1142/s0218127494001210.

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The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2×2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady p
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Delgado, Paul M., V. M. Krushnarao Kotteda, and Vinod Kumar. "Hybrid Fixed-Point Fixed-Stress Splitting Method for Linear Poroelasticity." Geosciences 9, no. 1 (2019): 29. http://dx.doi.org/10.3390/geosciences9010029.

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Efficient and accurate poroelasticity models are critical in modeling geophysical problems such as oil exploration, gas-hydrate detection, and hydrogeology. We propose an efficient operator splitting method for Biot’s model of linear poroelasticity based on fixed-point iteration and constrained stress. In this method, we eliminate the constraint on time step via combining our fixed-point approach with a physics-based restraint between iterations. Three different cases are considered to demonstrate the stability and consistency of the method for constant and variable parameters. The results are
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Robin, W. "Some remarks on the asymptotic iteration method." Journal of Innovative Technology and Education 3 (2016): 251–64. http://dx.doi.org/10.12988/jite.2016.6613.

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Ismail, Mourad E. H., and Nasser Saad. "A discrete and q asymptotic iteration method." Journal of Difference Equations and Applications 26, no. 4 (2020): 488–509. http://dx.doi.org/10.1080/10236198.2020.1748021.

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CIFTCI, HAKAN. "ANHARMONIC OSCILLATOR ENERGIES BY THE ASYMPTOTIC ITERATION METHOD." Modern Physics Letters A 23, no. 04 (2008): 261–67. http://dx.doi.org/10.1142/s0217732308024006.

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In a previous paper (J. Phys. A36, 11807 (2003)), the "asymptotic iteration method" was introduced and developed for solving second-order homogeneous linear differential equations. In this paper we use the method to study the quantum quartic anharmonic oscillator problem. We obtain accurate eigenvalues for both small and large coupling parameters.
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Mikulski, Damian, Marcin Molski, and Jerzy Konarski. "Supersymmetry quantum mechanics and the asymptotic iteration method." Journal of Mathematical Chemistry 46, no. 4 (2009): 1356–68. http://dx.doi.org/10.1007/s10910-009-9519-3.

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Lambaré, Gilles, Jean Virieux, Raul Madariaga, and Side Jin. "Iterative asymptotic inversion in the acoustic approximation." GEOPHYSICS 57, no. 9 (1992): 1138–54. http://dx.doi.org/10.1190/1.1443328.

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We propose an iterative method for the linearized prestack inversion of seismic profiles based on the asymptotic theory of wave propagation. For this purpose, we designed a very efficient technique for the downward continuation of an acoustic wavefield by ray methods. The different ray quantities required for the computation of the asymptotic inverse operator are estimated at each diffracting point where we want to recover the earth image. In the linearized inversion, we use the background velocity model obtained by velocity analysis. We determine the short wavelength components of the impedan
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Dissertations / Theses on the topic "Asymptotic Iteration Method"

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Aydogdu, Oktay. "Pseudospin Symmetry And Its Applications." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611298/index.pdf.

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The pseudospin symmetry concept is investigated by solving the Dirac equation for the exactly solvable potentials such as pseudoharmonic potential, Mie-type potential, Woods-Saxon potential and Hulth&eacute<br>n plus ring-shaped potential with any spin-orbit coupling term $kappa$. Nikiforov-Uvarov Method, Asymptotic Iteration Method and functional analysis method are used in the calculations. The energy eigenvalue equations of the Dirac particles are found and the corresponding radial wave functions are presented in terms of special functions. We look for the contribution of the ring-shaped p
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Singh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.

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The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods tha
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Huang, Teng-Rui, and 黃騰銳. "The Asymptotic Iteration Method (AIM) Applied to QNMs of Black Holes." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/26045708094180856499.

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碩士<br>淡江大學<br>物理學系碩士班<br>99<br>In this thesis we show how to use the asymptotic iteration method (AIM) to numerically calculate the quasinormal modes (QNMs) of different (Schwarzschild, Reissner-Nordström and Kerr) black holes in four-dimensional spacetime. For Schwarzschild black holes, we compute the quasinormal frequencies of the gravitational perturbations. For the Kerr black holes, we consider both the scalar and the gravitational cases. We discuss our results especially for the low-lying modes, and compare them to previously published results.
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Dudeja, Rishabh. "High-dimensional Asymptotics for Phase Retrieval with Structured Sensing Matrices." Thesis, 2021. https://doi.org/10.7916/d8-g75n-8x58.

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Phase Retrieval is an inference problem where one seeks to recover an unknown complex-valued 𝓃-dimensional signal vector from the magnitudes of 𝓶 linear measurements. The linear measurements are specified using a 𝓶 × 𝓃 sensing matrix. This problem is a mathematical model for imaging systems arising in X-ray crystallography and other applications where it is infeasible to acquire the phase of the measurements. This dissertation presents some results regarding the analysis of this problem in the high-dimensional asymptotic regime where the number of measurements and the signal dimension diverge
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Book chapters on the topic "Asymptotic Iteration Method"

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Kulikov, Gennady Yu, and Arkadi I. Merkulov. "Asymptotic Error Estimate of Iterative Newton-Type Methods and Its Practical Application." In Computational Science and Its Applications – ICCSA 2004. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24767-8_70.

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Fekri, Mohamed, and Anne Ruiz-Gazen. "A B-Robust Non-Iterative Scatter Matrix Estimator: Asymptotics and Application to Cluster Detection Using Invariant Coordinate Selection." In Modern Nonparametric, Robust and Multivariate Methods. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-22404-6_22.

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Ammari, Habib, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab. "Optimal Control Imaging of Extended Inclusions." In Mathematical Methods in Elasticity Imaging. Princeton University Press, 2015. http://dx.doi.org/10.23943/princeton/9780691165318.003.0010.

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This chapter describes the use of time-reversal imaging techniques for optimal control of extended inclusions. It first considers the problem of reconstructing shape deformations of an extended elastic target before reconstructing the perturbations from boundary measurements of the displacement field. As for small-volume inclusions, direct imaging algorithms based on an asymptotic expansion for the perturbations in the data due to small shape deformations is introduced. The chapter also presents a concept equivalent to the polarization tensor for small-volume inclusions as well as the nonlinear optimization problem for reconstructing the shape of an extended inclusion from boundary displacement measurements. Finally, it develops iterative algorithms to address the nonlinearity of the problem.
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Sikorski, Krzysztof A. "Introduction." In Optimal Solution of Nonlinear Equations. Oxford University Press, 2001. http://dx.doi.org/10.1093/oso/9780195106909.003.0004.

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This monograph is devoted to studying worst case complexity results and optimal or nearly optimal methods for the approximation of solutions of nonlinear equations, approximation of fixed points, and computation of the topological degree. The methods are “global” in nature. They guarantee that the computed solution is within a specified error from the exact solution for every function in a given class. A common approach in numerical analysis is to study the rate of convergence and/or locally convergent methods that require special assumptions on the location of initial points of iterations to be “sufficiently” close to the actual solutions. This approach is briefly reviewed in the annotations to chapter 2, as well as in section 2.1.6, dealing with the asymptotic analysis of the bisection method. Extensive literature exists describing the iterative approach, with several monographs published over the last 30 years. We do not attempt a complete review of this work. The reader interested in this classical approach should consult the monographs listed in the annotations to chapter 2. We motivate our analysis and introduce basic notions in a simple example of zero finding for continuous function with different signs at the endpoints of an interval. Example 3.1 We want to approximate a zero of a function f from the class F = {f : [0,1] → R : f(0) ,&lt; 0 and f(1) &gt; 0, continuous}.By an approximate solution of this problem we understand any point x = x (f) such that the distance between x and some zero ∝ = ∝(f) of the function f , f (∝ ) = 0, is at most equal to a given small positive number ∈,|x — ∝ ≤ ∈. To compute x we first gather some information on the function f by sampling f at n sequentially chosen points ti in the interval [0,1]. Then, based on this information we select x. To minimize the time complexity we must select the minimal number of sampling points, that guarantee computing x(f) for any function f in the class F. This minimal number of samples (in the worst case) is called the information complexity of the problem.
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Amine, Khalil. "Insights Into Simulated Annealing." In Advances in Computational Intelligence and Robotics. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-2857-9.ch007.

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Simulated annealing is a probabilistic local search method for global combinatorial optimisation problems allowing gradual convergence to a near-optimal solution. It consists of a sequence of moves from a current solution to a better one according to certain transition rules while accepting occasionally some uphill solutions in order to guarantee diversity in the domain exploration and to avoid getting caught at local optima. The process is managed by a certain static or dynamic cooling schedule that controls the number of iterations. This meta-heuristic provides several advantages that include the ability of escaping local optima and the use of small amount of short-term memory. A wide range of applications and variants have hitherto emerged as a consequence of its adaptability to many combinatorial as well as continuous optimisation cases, and also its guaranteed asymptotic convergence to the global optimum.
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Conference papers on the topic "Asymptotic Iteration Method"

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Kocak, G., and I. Boztosun. "Asymptotic Iteration Method Solution of the Supersymmetric Schrödinger Equation." In SIXTH INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. AIP, 2007. http://dx.doi.org/10.1063/1.2733190.

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Bayrak, O., and I. Boztosun. "Analytical Solution of the Morse and the Hulthén Potentials by using Asymptotic iteration Method." In SIXTH INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. AIP, 2007. http://dx.doi.org/10.1063/1.2733182.

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Oh, Changwon, Taewung Kim, Kwonshik Park, and Hyun-Yong Jeong. "A Simplified Hydroplaning Simulation for a Straight-Grooved Tire by Using FDM, FEM and an Asymptotic Method." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43358.

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Much research has been conducted to simulate the hydroplaning phenomenon of tires using commercial explicit FEM (finite element method) codes such as MSC.Dytran and LS-DYNA. However, it takes a long time to finish such a simulation because its model has a great number of Lagrangian and Eulerian elements and a contact should be defined between the two different types of elements, and the simulation results of the lift force and the contact force are oscillatory. Thus, in this study a new methodology was proposed for the hydroplaning simulation using two separate mathematical models; an FDM (fin
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Ouyang, P. R., W. J. Zhang, and Madan M. Gupta. "An Adaptive Evolutionary Switching Control for Robot Manipulators." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84333.

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In this paper, a new adaptive switching control approach, called adaptive evolutionary switching PD control (AES-PD), is proposed for iterative operations of robot manipulators. The proposed AES-PD control method is a combination of the feedback of PD control with gain switching and feedforward using the input torque profile obtained from the previous iteration. The asymptotic convergence of the AES-PD control method is theoretically proved using Lyapunov’s method. The philosophy of the switching control strategy is interpreted in the context of the iteration domain to increase the speed of th
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Husein, Andri S., C. Cari, A. Suparmi, and Miftachul Hadi. "Approximate solution wave propagation in TM mode through a graded interface of permittivity/permeability profile using asymptotic iteration method." In THE 4TH INTERNATIONAL CONFERENCE ON THEORETICAL AND APPLIED PHYSICS (ICTAP) 2014. AIP Publishing LLC, 2016. http://dx.doi.org/10.1063/1.4943743.

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Thompson, Lonny L., and Prapot Kunthong. "Stabilized Time-Discontinuous Galerkin Methods With Applications to Structural Acoustics." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-15753.

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The time-discontinuous Galerkin (TDG) method possesses high-order accuracy and desirable C-and L-stability for second-order hyperbolic systems including structural acoustics. C- and L-stability provide asymptotic annihilation of high frequency response due to spurious resolution of small scales. These non-physical responses are due to limitations in spatial discretization level for large-complex systems. In order to retain the high-order accuracy of the parent TDG method for high temporal approximation orders within an efficient multi-pass iterative solution algorithm which maintains stability
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Aygun, M., I. Boztosun та Y. Sahin. "The Energy Eigenvalues of V(r)=−Zr + gr + λr[sup 2] Potential In The Constant Homogeneous Magnetic Field By The Asymptotic Iteration Method". У SIXTH INTERNATIONAL CONFERENCE OF THE BALKAN PHYSICAL UNION. AIP, 2007. http://dx.doi.org/10.1063/1.2733181.

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Khanoki, Sajad Arabnejad, and Damiano Pasini. "Multiscale Design and Multiobjective Optimization of Orthopaedic Cellular Hip Implants." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47487.

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A multiscale design and multiobjective optimization procedure is developed to design a new type of graded cellular hip implant. We assume that the prosthesis design domain is occupied by a unit cell representing the building block of the implant. An optimization strategy seeks the best geometric parameters of the unit cell to minimize bone resorption and interface failure, two conflicting objective functions. Using the asymptotic homogenization method, the microstructure of the implant is replaced by a homogeneous medium with an effective constitutive tensor. This tensor is used to construct t
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Li, Daozhong, Stephen Roper, and Il Yong Kim. "Advanced Primal-Dual Interior-Point Method for the Method of Moving Asymptotes." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85379.

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The Method of Moving Asymptotes (MMA) is one of the well-known optimization algorithms for topology optimization due to its stable numerical performance. Here, this paper simplifies the MMA algorithm by considering the features of topology optimization problem statements and presents a strategy to solve the necessary subproblems based on the primal-dual-interior-point method to further enhance numerical performance. A new scaling mechanism is also introduced to improve searching quality by utilizing the sensitivities of the original problems at the beginning of each MMA iteration. Numerical ex
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Geiser, Jürgen. "Iterative splitting method as almost asymptotic symplectic integrator for stochastic nonlinear Schrödinger equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992688.

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