Fast algorithms for high-order spline collocation systems
type: Item
instance of: scholarly article
title: Fast algorithms for high-order spline collocation systems
zbMATH Open document ID: 0929.65103
author: K. Appert
published in: Numerische Mathematik
publication date: 2000-02-02T00:00:00Z
review text: Well-known fast direct algorithms have been developed for low-order discretizations to solve elliptic partial differential equations. A low-order discretization often gives a simple matrix structure. Development in this area has been described by \textit{R. W. Hockney} [J. Assoc. Comput. Machin. 12, 95-113 (19965; Zbl 0139.10902)], \textit{F. W. Dorr} [SIAM Rev. 12, 248-263 (1970; Zbl 0208.42403)], \textit{J. R. Rice} and \textit{R. F. Boisert} [Solving elliptic problems using ELLPACK (1985; Zbl 0562.65064)] and others. In this paper the author presents a complete eigenvalue analysis for arbitrary \(C^1\)-spline collocation methods applied to the Poisson equation on a rectangular domain with Dirichlet boundary conditions. Based on this analysis, the author develops some fast algorithms to solve a class of high-order spline collocation systems which arise from discretizing the Poisson equation.
reviewed by: V. V. Strygin
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 1251318
zbMATH Keywords: spline collocation methods
zbMATH Keywords: fast direct algorithms
zbMATH Keywords: elliptic partial differential equations
zbMATH Keywords: eigenvalue analysis
zbMATH Keywords: Poisson equation
describes a project that uses: ELLPACK
describes a project that uses: COLSYS
MaRDI profile type: Publication
full work available at URL: s002110050387
OpenAlex ID: W2046703156
DOI: 10.1007/S002110050387
description: scientific article; zbMATH DE number 1251318