Results 1 to 10 of about 1,594 (139)
Mathematical and Computational ApplicationsThis paper aims to systematically assess the local radial basis function collocation method, structured with multiquadrics (MQs) and polyharmonic splines (PHSs), for solving steady and transient diffusion problems.
Božidar Šarler +2 more
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Mathematics and Computers in SimulationUnisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the ...
Roberto Cavoretto +2 more
exaly +6 more sources
Cardinal interpolation with general multiquadrics [PDF]
Advances in Computational Mathematics, 2015 This paper studies the cardinal interpolation operators associated with the general multiquadrics, ϕα, c(x)=(∥x∥2 + c2)α, x∈ℝd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage ...
Keaton Hamm, J. Ledford
semanticscholar +5 more sources
Computational issues by interpolating with inverse multiquadrics: a solution [PDF]
CoRR, 2022 We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods.
S. Marchi +4 more
semanticscholar +5 more sources
Cardinal interpolation with general multiquadrics: convergence rates [PDF]
Advances in Computational Mathematics, 2015 This article pertains to interpolation of Sobolev functions at shrinking lattices hℤd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage ...
Keaton Hamm, J. Ledford
semanticscholar +5 more sources
Adaptive Interpolation by Scaled Multiquadrics
Advances in Computational Mathematics, 2002 Given a univariate data sample, the authors present an adaptative method to select a subsample in such a way that shape preserving information is extracted, that is to say, that the interpolating function constructed by the subsample reproduces the signal with a good graphical accuracy.
M. Bozzini, L. Lenarduzzi, R. Schaback
semanticscholar +5 more sources
On Shifted Cardinal Interpolation by Gaussians and Multiquadrics
Journal of Approximation Theory, 1996 The authors study so-called shifted Gaussian interpolation where approximants are given as a (finite or infinite) linear combination of translates of some Gaussian. More precisely, the approximants \(s\) are of the form \[ s(x)= \sum_{k\in\mathbb{Z}^d} a_k \varphi(x+\alpha-k) \qquad (x\in\mathbb{R}^d), \tag{1} \] where \(\mathbb{Z}\) is the set of ...
B. Baxter, N. Sivakumar
semanticscholar +3 more sources
Analytical Particular Solutions of Multiquadrics Associated with Polyharmonic Operators [PDF]
Mathematical Problems in Engineering, 2013 We derive two- and three-dimensional analytical particular solutions of multiquadrics (MQ) associated with the polyharmonic operators, named as the polyharmonic multiquadrics (PMQs).
C. Tsai
semanticscholar +3 more sources
High Accuracy Quasi-Interpolation using a new class of generalized Multiquadrics [PDF]
arXiv.org, 2023 A new generalization of multiquadric functions $\phi(x)=\sqrt{c^{2d}+||x||^{2d}}$, where $x\in\mathbb{R}^n$, $c\in \mathbb{R}$, $d\in \mathbb{N}$, is presented to increase the accuracy of quasi-interpolation further.
Mathis Ortmann, M. Buhmann
semanticscholar +1 more source
High accuracy quasi-interpolation using a new class of generalized multiquadrics
Journal of Mathematical Analysis and ApplicationsMartin Buhmann
exaly +2 more sources