Relevant bibliographies by topics / Local interpolation error,estimates

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  1. Journal articles
  2. Dissertations / Theses
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  5. Conference papers

Academic literature on the topic 'Local interpolation error,estimates'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Local interpolation error,estimates"

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Zuppa, Carlos. "Error estimates for modified local Shepard's interpolation formula." Applied Numerical Mathematics 49, no. 2 (2004): 245–59. http://dx.doi.org/10.1016/j.apnum.2003.11.001.

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Etherington, Thomas R. "Discrete natural neighbour interpolation with uncertainty using cross-validation error-distance fields." PeerJ Computer Science 6 (July 13, 2020): e282. http://dx.doi.org/10.7717/peerj-cs.282.

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Interpolation techniques provide a method to convert point data of a geographic phenomenon into a continuous field estimate of that phenomenon, and have become a fundamental geocomputational technique of spatial and geographical analysts. Natural neighbour interpolation is one method of interpolation that has several useful properties: it is an exact interpolator, it creates a smooth surface free of any discontinuities, it is a local method, is spatially adaptive, requires no statistical assumptions, can be applied to small datasets, and is parameter free. However, as with any interpolation method, there will be uncertainty in how well the interpolated field values reflect actual phenomenon values. Using a method based on natural neighbour distance based rates of error calculated for data points via cross-validation, a cross-validation error-distance field can be produced to associate uncertainty with the interpolation. Virtual geography experiments demonstrate that given an appropriate number of data points and spatial-autocorrelation of the phenomenon being interpolated, the natural neighbour interpolation and cross-validation error-distance fields provide reliable estimates of value and error within the convex hull of the data points. While this method does not replace the need for analysts to use sound judgement in their interpolations, for those researchers for whom natural neighbour interpolation is the best interpolation option the method presented provides a way to assess the uncertainty associated with natural neighbour interpolations.
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Li, Ming, and Feilong Cao. "Local uniform error estimates for spherical basis functions interpolation." Mathematical Methods in the Applied Sciences 37, no. 9 (2013): 1364–76. http://dx.doi.org/10.1002/mma.2898.

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Hetmaniuk, U., and P. Knupp. "Local Anisotropic Interpolation Error Estimates Based on Directional Derivatives Along Edges." SIAM Journal on Numerical Analysis 47, no. 1 (2009): 575–95. http://dx.doi.org/10.1137/060666524.

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WU, ZONG-MIN, and ROBERT SCHABACK. "Local error estimates for radial basis function interpolation of scattered data." IMA Journal of Numerical Analysis 13, no. 1 (1993): 13–27. http://dx.doi.org/10.1093/imanum/13.1.13.

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HESSE, KERSTIN, and Q. T. LE GIA. "LOCAL RADIAL BASIS FUNCTION APPROXIMATION ON THE SPHERE." Bulletin of the Australian Mathematical Society 77, no. 2 (2008): 197–224. http://dx.doi.org/10.1017/s0004972708000087.

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AbstractIn this paper we derive local error estimates for radial basis function interpolation on the unit sphere $\mathbb {S}^2\subset \mathbb {R}^3$. More precisely, we consider radial basis function interpolation based on data on a (global or local) point set $X\subset \mathbb {S}^2$ for functions in the Sobolev space $H^s(\mathbb {S}^2)$ with norm $\|\cdot \|_s$, where s>1. The zonal positive definite continuous kernel ϕ, which defines the radial basis function, is chosen such that its native space can be identified with $H^s(\mathbb {S}^2)$. Under these assumptions we derive a local estimate for the uniform error on a spherical cap S(z;r): the radial basis function interpolant ΛXf of $f\in H^s(\mathbb {S}^2)$ satisfies $\sup _{\mathbf {x}\in S(\mathbf {z};r)} |f(\mathbf {x})-\Lambda _X f(\mathbf {x})| \leq c h^{(s-1)/2} \|f\|_{s}$, where h=hX,S(z;r) is the local mesh norm of the point set X with respect to the spherical cap S(z;r). Our proof is intrinsic to the sphere, and makes use of the Videnskii inequality. A numerical test illustrates the theoretical result.
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Hedger, Richard D., François Martin, Julian J. Dodson, Daniel Hatin, François Caron, and Fred G. Whoriskey. "The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers." ICES Journal of Marine Science 65, no. 7 (2008): 1248–59. http://dx.doi.org/10.1093/icesjms/fsn109.

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Abstract Hedger, R. D., Martin, F., Dodson, J, J., Hatin, D., Caron, F., and Whoriskey, F. G. 2008. The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers. – ICES Journal of Marine Science, 65: 1248–1259. The principal method for interpolating the positions and speeds of tagged fish within an array of fixed acoustic receivers is the weighted-mean method, which uses a box-kernel estimator, one of the simplest smoothing options available. This study aimed to determine the relative error of alternative, non-parametric regression methods for estimating these parameters. It was achieved by predicting the positions and speeds of three paths made through a dense array of fixed acoustic receivers within a coastal embayment (Gaspé Bay, Québec, Canada) by a boat with a GPS trailing an ultrasonic transmitter. Transmitter positions and speeds were estimated from the receiver data using kernel estimators, with box and normal kernels and the kernel size determined arbitrarily, and by several non-parametric methods, i.e. a kernel estimator, a smoothing spline, and local polynomial regression, with the kernel size or smoothing span determined by cross-validation. Prediction error of the kernel estimator was highly dependent upon kernel size, and a normal kernel produced less error than the box kernel. Of the methods using cross-validation, local polynomial regression produced least error, suggesting it as the optimal method for interpolation. Prediction error was also strongly dependent on array density. The local polynomial regression method was used to determine the movement patterns of a sample of tagged Atlantic salmon (Salmo salar) smolt and kelt, and American eel (Anguilla rostrata). Analysis of the estimates from local polynomial regression suggested that this was a suitable method for monitoring patterns of fish movement.
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Kamata, Keisuke, Koichi Kinoshita, and Manabu Kano. "Missing RRI Interpolation Algorithm based on Locally Weighted Partial Least Squares for Precise Heart Rate Variability Analysis." Sensors 18, no. 11 (2018): 3870. http://dx.doi.org/10.3390/s18113870.

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The R-R interval (RRI) fluctuation in electrocardiogram (ECG) is called heart rate variability (HRV), which reflects activities of the autonomic nervous system (ANS) and has been used for various health monitoring services. Accurate R wave detection is crucial for success in HRV-based health monitoring services; however, ECG artifacts often cause missing R waves and deteriorate the accuracy of HRV analysis. The present work proposes a new missing RRI interpolation technique based on Just-In-Time (JIT) modeling. In the JIT modeling framework, a local regression model is built by weighing samples stored in the database according to the distance from a query and output is estimated only when an estimate is requested. The proposed method builds a local model and estimates missing RRI only when an RRI detection error is detected. Locally weighted partial least squares (LWPLS) is adopted for local model construction. The proposed method is referred to as LWPLS-based RRI interpolation (LWPLS-RI). The performance of the proposed LWPLS-RI was evaluated through its application to RRI data with artificial missing RRIs. We used the MIT-BIH Normal Sinus Rhythm Database for nominal RRI dataset construction. Missing RRIs were artificially introduced and they were interpolated by the proposed LWPLS-RI. In addition, MEAN that replaces the missing RRI by a mean of the past RRI data was compared as a conventional method. The result showed that the proposed LWPLS-RI improved root mean squared error (RMSE) of RRI by about 70% in comparison with MEAN. In addition, the proposed method realized precise HRV analysis. The proposed method will contribute to the realization of precise HRV-based health monitoring services.
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Fonseca, Kalina, Mercy IlbayYupa, Luis Bustillos, Sara Barbosa, and Alisson Iza. "Comparación de Métodos de Interpolación para la Estimación de Temperatura del Reservorio CEASA." Revista Bases de la Ciencia. e-ISSN 2588-0764 3, no. 1 (2018): 57. http://dx.doi.org/10.33936/rev_bas_de_la_ciencia.v3i1.1108.

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La interpolación de temperatura en cuerpos de agua permite realizar predicciones de puntos de muestreo que no presentan datos. En la presente investigación se evaluaron 12 métodos de interpolación para estimar la temperatura del reservorio del Centro de Experimentación Académica Salache (CEASA) de la Universidad Técnica de Cotopaxi. Los datos recolectados en campo fueron interpolados aleatoriamente y comparados con los reales en base al error medio (EM), error absoluto medio (MAE), error medio cuadrático (MSE), raíz del error cuadrático (RMSE) y coeficiente de determinación (R2). La interpolación más apropiada para la representación de la variable temperatura en el reservorio fue el del método del Polinomio Local con un MSE de 0,22 y RMSE de 0,47 y R2 de 0,53. Este método se puede utilizar para obtener datos de temperatura del reservorio, disminuyendo costos de tiempo y dinero que demandaría el levantamiento de información en campo.
 Palabras clave: Interpolación, Temperatura, Polinomio Local, Reservorio CEASA. 
 
 ABSTRACT
 The interpolation of temperature in bodies of water allows making predictions of sampling points that do not present data. In the present investigation, 12 interpolation methods were evaluated to estimate the reservoir temperature of the Salache Academic Experimentation Center (CEASA) at the Technical University of Cotopaxi. The data collected in the field were randomly interpolated and compared with the real ones based on the mean error (MS), mean absolute error (MAE), mean square error (MSE), the root of the quadratic error (RMSE) and coefficient of determination (R2). The most appropriate interpolation for the representation of the variable temperature in the reservoir was the Local Polynomial method with an MSE of 0.22 and RMSE of 0.47 and R2 of 0.53. This method can be used to obtain reservoir temperature data, decreasing the time and money costs that gathering information would require in the field require.
 Key words: Interpolation, Temperature, Local Polynomial, CEASA Reservoir.
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Khan, Suliman, M. Riaz Khan, Aisha M. Alqahtani, et al. "A well-conditioned and efficient implementation of dual reciprocity method for Poisson equation." AIMS Mathematics 6, no. 11 (2021): 12560–82. http://dx.doi.org/10.3934/math.2021724.

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<abstract><p>One of the attractive and practical techniques to transform the domain integrals to equivalent boundary integrals is the dual reciprocity method (DRM). The success of DRM relies on the proper treatment of the non-homogeneous term in the governing differential equation. For this purpose, radial basis functions (RBFs) interpolations are performed to approximate the non-homogeneous term accurately. Moreover, when the interpolation points are large, the global RBFs produced dense and ill-conditioned interpolation matrix, which poses severe stability and computational issues. Fortunately, there exist interpolation functions with local support known as compactly supported radial basis functions (CSRBFs). These functions produce a sparse and well-conditioned interpolation matrix, especially for large-scale problems. Therefore, this paper aims to apply DRM based on multiquadrics (MQ) RBFs and CSRBFs for evaluation of the Poisson equation, especially for large-scale problems. Furthermore, the convergence analysis of DRM with MQ and CSRBFs is performed, along with error estimate and stability analysis. Several experiments are performed to ensure the well-conditioned, efficient, and accurate behavior of the CSRBFs compared to the MQ-RBFs, especially for large-scale interpolation points.</p></abstract>
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Dissertations / Theses on the topic "Local interpolation error,estimates"

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Apel, Th. "Interpolation of non-smooth functions on anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801341.

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In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed. The modified operators are defined for non-smooth functions and are suited for the application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.
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Apel, T., and S. Nicaise. "Elliptic problems in domains with edges: anisotropic regularity and anisotropic finite element meshes." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800553.

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This paper is concerned with the anisotropic singular behaviour of the solution of elliptic boundary value problems near edges. The paper deals first with the description of the analytic properties of the solution in newly defined, anisotropically weighted Sobolev spaces. The finite element method with anisotropic, graded meshes and piecewise linear shape functions is then investigated for such problems; the schemes exhibit optimal convergence rates with decreasing mesh size. For the proof, new local interpolation error estimates in anisotropically weighted spaces are derived. Moreover, it is shown that the condition number of the stiffness matrix is not affected by the mesh grading. Finally, a numerical experiment is described, that shows a good agreement of the calculated approximation orders with the theoretically predicted ones.
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Gillette, Andrew, and Alexander Rand. "INTERPOLATION ERROR ESTIMATES FOR HARMONIC COORDINATES ON POLYTOPES." EDP SCIENCES S A, 2016. http://hdl.handle.net/10150/621355.

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Interpolation error estimates in terms of geometric quality measures are established for harmonic coordinates on polytopes in two and three dimensions. First we derive interpolation error estimates over convex polygons that depend on the geometric quality of the triangles in the constrained Delaunay triangulation of the polygon. This characterization is sharp in the sense that families of polygons with poor quality triangles in their constrained Delaunay triangulations are shown to produce large error when interpolating a basic quadratic function. Non-convex polygons exhibit a similar limitation: large constrained Delaunay triangles caused by vertices approaching a non-adjacent edge also lead to large interpolation error. While this relationship is generalized to convex polyhedra in three dimensions, the possibility of sliver tetrahedra in the constrained Delaunay triangulation prevent the analogous estimate from sharply reflecting the actual interpolation error. Non-convex polyhedra are shown to be fundamentally different through an example of a family of polyhedra containing vertices which are arbitrarily close to non-adjacent faces yet the interpolation error remains bounded.
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Apel, Thomas, and Cornelia Pester. "Clément-type interpolation on spherical domains - interpolation error estimates and application to a posteriori error estimation." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601335.

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In this paper, a mixed boundary value problem for the Laplace-Beltrami operator is considered for spherical domains in $R^3$, i.e. for domains on the unit sphere. These domains are parametrized by spherical coordinates (\varphi, \theta), such that functions on the unit sphere are considered as functions in these coordinates. Careful investigation leads to the introduction of a proper finite element space corresponding to an isotropic triangulation of the underlying domain on the unit sphere. Error estimates are proven for a Clément-type interpolation operator, where appropriate, weighted norms are used. The estimates are applied to the deduction of a reliable and efficient residual error estimator for the Laplace-Beltrami operator.
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Apel, Th. "A note on anisotropic interpolation error estimates for isoparametric quadrilateral finite elements." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801071.

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Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian finite elements with straight edges. These elements are allowed to have diameters with different asymptotic behaviour in different space directions. The case of affine elements (parallelepipeds) with arbitrarily high degree of the shape functions is considered first. Then, a careful examination of the multi-linear map leads to estimates for certain classes of more general, isoparametric elements. As an application, the Galerkin finite element method for a reaction diffusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.
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Brownlee, Robert Alexander. "Error estimates for interpolation of rough and smooth functions using radial basis functions." Thesis, University of Leicester, 2004. http://hdl.handle.net/2381/8825.

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In this thesis we are concerned with the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the interpolation points fill out a bounded domain in Euclidean space. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function - the native space. This work establishes Lp-error estimates, for 1 ≤ p ≤ ∞, when the function being interpolated fails to have the required smoothness to lie in the corresponding native space; therefore, providing error estimates for a class of rougher functions than previously known. Such estimates have application in the numerical analysis of solving partial differential equations using radial basis function collocation methods. At first our discussion focuses on the popular polyharmonic splines. A more general class of radial basis functions is admitted into exposition later on, this class being characterised by the algebraic decay of the Fourier transform of the radial basis function. The new estimates presented here offer some improvement on recent contributions from other authors by having wider applicability and a more satisfactory form. The method of proof employed is not restricted to interpolation alone. Rather, the technique provides error estimates for the approximation of rough functions for a variety of related approximation schemes as well. For the previously mentioned class of radial basis functions, this work also gives error estimates when the function being interpolated has some additional smoothness. We find that the usual Lp-error estimate, for 1 ≤ p ≤ ∞, where the approximand belongs to the corresponding native space, can be doubled. Furthermore, error estimates are established for functions with smoothness intermediate to that of the native space and the subspace of the native space where double the error is observed.
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Kirby, Robert Charles. "Local time stepping and a posteriori error estimates for flow and transport in porous media /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.

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Carson, Hugh Alexander. "A priori analysis of global and local output error estimates for CG, DG and HDG finite element discretizations." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105608.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 103-105).<br>In this thesis, a priori convergence estimates are developed for outputs, output error estimates, and localizations of output error estimates for Galerkin finite element methods. Specifically, Continuous Galerkin (CG), Discontinuous Galerkin (DG), and Hybridized DG (HDG) methods are analyzed for the Poisson problem. A mixed formulation for DG output error estimation is proposed with improved convergence rates relative to the common approach utilizing statically condensed, p-dependent lifting operators. The HDG output error estimates are new and include the impact of stabilization. Comparisons to numerical results demonstrate (1) the sharpness of the estimates and (2) that the HDG estimates are approximately an order of magnitude more accurate than CG and DG.<br>by Hugh Alexander Carson.<br>S.M.
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Lacouture, Loïc. "Modélisation et simulation du mouvement de structures fines dans un fluide visqueux : application au transport mucociliaire." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS139/document.

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Une grande part des muqueuses à l’intérieur du corps humain sont recouvertes de cils qui, par leurs mouvements coordonnés, conduisent à une circulation de la couche de fluide nappant la muqueuse. Dans le cas de la paroi interne des bronches, ce processus permet l’évacuation des impuretés inspirées à l’extérieur de l’appareil respiratoire.Dans cette thèse, nous nous intéressons aux effets du ou des cils sur le fluide, en nous plaçant à l’échelle du cil, et on considère pour cela les équations de Stokes incompressible. Due à la finesse du cil, une simulation directe demanderait un raffinement important du maillage au voisinage du cil, pour un maillage qui évoluerait à chaque pas de temps. Cette approche étant trop onéreuse en terme de coûts de calculs, nous avons considéré l’asymptotique d’un diamètre du cil tendant vers 0 et d’une vitesse qui tend vers l’infini : le cil est modélisé par un Dirac linéique de forces en terme source. Nous avons montré qu’il était possible de remplacer ce Dirac linéique par une somme de Dirac ponctuels distribués le long du cil. Ainsi, nous nous sommes ramenés, par linéarité, à étudier le problème de Stokes avec en terme source une force ponctuelle. Si les calculs sont ainsi simplifiés (et leurs coûts réduits), le problème final est lui plus singulier, ce qui motive une analyse numérique fine et l’élaboration d’une nouvelle méthode de résolution.Nous avons d’abord étudié une version scalaire de ce problème : le problème de Poisson avec une masse de Dirac en second membre. La solution exacte étant singulière, la solution éléments finis est à définir avec précaution. La convergence de la méthode étant dégradée dans ce cas-là, par rapport à celle dans le cas régulier, nous nous sommes intéressés à des estimations locales. Nous avons démontré une convergence quasi-optimale en norme Hs (s ě 1) sur un sous-domaine qui exclut la singularité. Des résultats analogues ont été obtenus dans le cas du problème de Stokes.Pour palier les problèmes liés à une mauvais convergence sur l’ensemble du domaine, nous avons élaboré une méthode pour résoudre des problème elliptiques avec une masse de Dirac ou une force ponctuelle en terme source. Basée sur celle des éléments finis standard, elle s’appuie sur la connaissance explicite de la singularité de la solution exacte. Une fois données la position de chacun des cils et leur paramétrisation, notre méthode rend possible la simulation directe en 3d d’un très grand nombre de cils. Nous l’avons donc appliquée au cas du transport mucociliaire dans les poumons. Cet outil numérique nous donne accès à des informations que l’on ne peut avoir par l’expérience, et permet de simuler des cas pathologiques comme par exemple une distribution éparse des cils<br>Numerous mucous membranes inside the human body are covered with cilia which, by their coordinated movements, lead to a circulation of the layer of fluid coating the mucous membrane, which allows, for example, in the case of the internal wall of the bronchi, the evacuation of the impurities inspired outside the respiratory system.In this thesis, we integrate the effects of the cilia on the fluid, at the scale of the cilium. For this, we consider the incompressible Stokes equations. Due to the very small thickness of the cilia, the direct computation would request a time-varying mesh grading around the cilia. To avoid too prohibitive computational costs, we consider the asymptotic of a zero diameter cilium with an infinite velocity: the cilium is modelled by a lineic Dirac of force in source term. In order to ease the computations, the lineic Dirac of forces can be approached by a sum of punctual Dirac masses distributed along the cilium. Thus, by linearity, we have switched our initial problem with the Stokes problem with a punctual force in source term. Thus, we simplify the computations, but the final problem is more singular than the initial problem. The loss of regularity involves a deeper numerical analysis and the development of a new method to solve the problem.We have first studied a scalar version of this problem: Poisson problem with a Dirac right-hand side. The exact solution is singular, therefore the finite element solution has to be defined with caution. In this case, the convergence is not as good as in the regular case, and thus we focused on local error estimates. We have proved a quasi-optimal convergence in H1-norm (s ď 1) on a sub-domain which does not contain the singularity. Similar results have been shown for the Stokes problem too.In order to recover an optimal convergence on the whole domain, we have developped a numerical method to solve elliptic problems with a Dirac mass or a punctual force in source term. It is based on the standard finite element method and the explicit knowl- edge of the singularity of the exact solution. Given the positions of the cilia and their parametrisations, this method permits to compute in 3d a very high number of cilia. We have applied this to the study of the mucociliary transport in the lung. This numerical tool gives us information we do not have with the experimentations and pathologies can be computed and studied by this way, like for example a small number of cilia
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Books on the topic "Local interpolation error,estimates"

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Apel, Thomas. Anisotropic finite elements: Local estimates and applications. B.G. Teubner, 1999.

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Tadmor, Eitan. Local error estimates for discontinuous solutions of nonlinear hyperbolic equations. Institute for Computer Applications in Science and Engineering, 1989.

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Center, Langley Research, ed. Local error estimates for discontinuous solutions of nonlinear hyperbolic equations. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Book chapters on the topic "Local interpolation error,estimates"

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Maz’ya, Vladimir, and Gunther Schmidt. "Error estimates for quasi-interpolation." In Approximate Approximations. American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/141/02.

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Amadori, Debora, and Laurent Gosse. "Local and Global Error Estimates." In SpringerBriefs in Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24785-4_2.

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Bank, Randolph E. "A-posteriori error estimates. Adaptive local mesh refinement and multigrid iteration." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0072638.

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Schulz, H., and W. L. Wendland. "Local, Residual-Based A Posteriori Error Estimates Forcing Adaptive Boundary Element Methods." In Boundary Element Topics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60791-2_21.

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Tscherning, C. C. "Improvement of Least-Squares Collocation Error Estimates Using Local GOCE T zz Signal Standard Deviations." In VIII Hotine-Marussi Symposium on Mathematical Geodesy. Springer International Publishing, 2015. http://dx.doi.org/10.1007/1345_2015_70.

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Amano, K., M. Asaduzzaman, T. Ooura, and S. Saitoh. "Representations of Analytic Functions on Typical Domains in Terms of Local Values and Truncation Error Estimates." In Analytic Extension Formulas and their Applications. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4757-3298-6_2.

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Akin, J. E. "Element interpolation and local coordinates." In Finite Element Analysis with Error Estimators. Elsevier, 2005. http://dx.doi.org/10.1016/b978-075066722-7/50034-5.

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Buhmann, M. D., and N. Dyn. "Error Estimates for Multiquadric Interpolation." In Curves and Surfaces. Elsevier, 1991. http://dx.doi.org/10.1016/b978-0-12-438660-0.50013-3.

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"ERROR ESTIMATES IN POLYNOMIAL INTERPOLATION." In Boundary Value Problems from Higher Order Differential Equations. WORLD SCIENTIFIC, 1986. http://dx.doi.org/10.1142/9789814415477_0008.

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Madych, W. R. "Error Estimates for Interpolation by Generalized Splines." In Curves and Surfaces. Elsevier, 1991. http://dx.doi.org/10.1016/b978-0-12-438660-0.50047-9.

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Conference papers on the topic "Local interpolation error,estimates"

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Sirikham, Adisorn, and Wuttipong Kumwilaisak. "Image Error Concealment Using Optimized Local Pixel Matching and Directional Interpolation." In The 9th International Conference on Advanced Communication Technology. IEEE, 2007. http://dx.doi.org/10.1109/icact.2007.358514.

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Sireta, François-Xavier, Quentin Derbanne, Fabien Bigot, Šime Malenica, and Eric Baudin. "Hydroelastic Response of a Ship Structural Detail to Seakeeping Loads Using a Top-Down Scheme." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83560.

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In order to investigate the local response of a ship structure, it is necessary to transfer the seakeeping loading to a 3DFEM model of the structure. A common approach is to transfer the seakeeping loads calculated by a BEM method to the FEM model. Following the need to take into account the dynamic response of the ship to the wave excitation, some methods based on a modal approach have been recently developed that include the dry structural modes in the hydro-structure coupling procedure and allow to compute the springing and whipping response of the ship structure to the seakeeping loads. In the context of the fatigue life assessment of a structural detail, a very fine FE model is required. A very large number of seakeeping loading cases also need to be considered to account for all the conditions encountered by the ship through its life. It becomes then clear that because of the CPU time issue, the whole FE model can not be very fine. This is why a hierarchical top-down analysis procedure is commonly used, in which the global ship structure is modelled in a coarse manner using one finite element between web frames. The structural details are modelled separately using a fine meshing. Such top-down methods are commonly used for the estimation of the quasi-static response of structural details to the seakeeping loads. This paper presents a methodology in which a top-down method is used to estimate the springing response of a ship structural detail loaded with wave pressure, and its fatigue life. The global dry structural modes are transferred to the detail fine model using the shape functions of the finite elements of the global model. The hydrodynamic pressures are computed directly on the fine mesh model, avoiding any interpolation error. The imposed displacements at the fine mesh boundary are computed using the same method that is used to transfer the structural mode shapes, and the local pressure induced loads and inertia loads are applied on the fine mesh nodes. This method is applied for the calculation of the elongation of a strain gauge which is installed in the passage way of an ultra large container ship.
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Caluwaerts, Ken, and Jochen J. Steil. "Independent joint learning in practice: Local error estimates to improve inverse dynamics control." In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids). IEEE, 2015. http://dx.doi.org/10.1109/humanoids.2015.7363439.

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Kreinovich, V. Ya. "Global Independence, Possible Local Dependence: Towards More Realistic Error Estimates for Indirect Measurements." In 2019 XXII International Conference on Soft Computing and Measurements (SCM). IEEE, 2019. http://dx.doi.org/10.1109/scm.2019.8903841.

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Moller, T., R. Machiraju, K. Mueller, and R. Yagel. "Classification and local error estimation of interpolation and derivative filters for volume rendering." In Proceedings of 1996 Symposium on Volume Visualization. IEEE, 1996. http://dx.doi.org/10.1109/svv.1996.558045.

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Hema, N., and Krishna Kant. "Local weather interpolation using remote AWS data with error corrections using sparse WSN for automated irrigation for Indian farming." In 2014 Seventh International Conference on Contemporary Computing (IC3). IEEE, 2014. http://dx.doi.org/10.1109/ic3.2014.6897220.

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Thompson, Lonny L., and Dantong He. "Local Space-Time Adaptive Discontinuous Galerkin Finite Element Methods for Time-Dependent Waves." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42542.

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Local space-time adaptive methods are developed including high-order accurate nonreflecting boundary conditions (NRBC) for time-dependent waves. The time-discontinuous Galerkin (TDG) variational method is used to divide the time-interval into space-time slabs, the solution advanced from one slab to the next. Within each slab, a continuous space-time mesh is used which enables local sub-time steps. By maintaining orthogonality of the space-time mesh and pre-integrating analytically through the time-slab, we obtain an efficient yet robust local space-time adaptive method. Any standard spatial element may be used together with standard spatial mesh generation and visualization methods. Recovery based error estimates are used in both space and time dimensions to determine the number and size of local space-time elements within a global time step such that both the spatial and temporal estimated error is equally distributed throughout the space-time approximation. The result is an efficient and reliable adaptive strategy which distributes local space-time elements where needed to accurately track time-dependent waves over large distances and time. Numerical examples of time-dependent acoustic radiation are given which demonstrate the accuracy, reliability and efficiency gained from this new technology.
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Subbarayalu, Sethuramalingam, and Lonny L. Thompson. "HP-Adaptive Time-Discontinuous Galerkin Finite Element Methods for Time-Dependent Waves." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60403.

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hp-Adaptive time-discontinuous Galerkin methods are developed for second-order hyperbolic systems. Explicit a priori error estimates in terms of time-step size, approximation order, and solution regularity are derived. Knowledge of these a priori convergence rates in combination with a posteriori error estimates computed from the jump in time-discontinuous solutions are used to automatically select time-step size h and approximation order p to achieve a specified error tolerance with a minimal number of total degrees-of-freedom. We show that the temporal jump error is a good indicator of the local error, and the summation of jump error for the total interval is good indicator for the global and accumulation errors. In addition, the accumulation error at the end of a time-step can be estimated well by the summation of the local jump error at the beginning of a time-step provided the approximation order is greater or equal to the solution regularity. Superconvergence of the end points of a time-step for high-order polynomials are also demonstrated.
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Park, Chanyoung, Nam H. Kim, and Raphael T. Haftka. "Least Bumpiness Calibration With Extrapolative Bias Correction." 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/detc2018-86163.

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Bias correction is important for model calibration to obtain unbiased calibration parameter estimates and make accurate prediction. However, calibration often relies on insufficient samples, and so bias correction often mostly depends on extrapolation. For example, bias correction with twelve samples in nine-dimensional box generated by Latin Hypercube Sampling (LHS) has less than 0.1% interpolation domain in the box. Since bias correction is coupled with calibration parameter estimation, calibration with extrapolative bias correction can lead a large error in the calibrated parameters. This paper proposes an idea of calibration with minimum bumpiness correction. The bumpiness of bias correction is a good measure of assessing the potential risk of a large error in the correction. By minimizing bumpiness, the risk of extrapolation can be reduced while the accuracy of parameter estimates can be achieved. It was found that this calibration method gave more accurate results than Bayesian calibration for an analytical example. It was also found that there are common denominators between the proposed method and the Bayesian calibration with bias correction.
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McCusker, James R., and Kourosh Danai. "Integrating Parameter Estimation Solutions From the Time and Time-Scale Domains." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2552.

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A method of parameter estimation was recently introduced that separately estimates each parameter of the dynamic model [1]. In this method, regions coined as parameter signatures, are identified in the time-scale domain wherein the prediction error can be attributed to the error of a single model parameter. Based on these single-parameter associations, individual model parameters can then be estimated for iterative estimation. Relative to nonlinear least squares, the proposed Parameter Signature Isolation Method (PARSIM) has two distinct attributes. One attribute of PARSIM is to leave the estimation of a parameter dormant when a parameter signature cannot be extracted for it. Another attribute is independence from the contour of the prediction error. The first attribute could cause erroneous parameter estimates, when the parameters are not adapted continually. The second attribute, on the other hand, can provide a safeguard against local minima entrapments. These attributes motivate integrating PARSIM with a method, like nonlinear least-squares, that is less prone to dormancy of parameter estimates. The paper demonstrates the merit of the proposed integrated approach in application to a difficult estimation problem.
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