Paper Info
Title
Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems
Abstract
Fast direct methods are presented for the solution of linear systems arising in high-order, tensor-product orthogonal spline collocation applied to separable, second order, linear, elliptic partial differential equations on rectangles. The methods, which are based on a matrix decomposition approach, involve the solution of a generalized eigenvalue problem corresponding to the orthogonal spline collocation discretization of a two-point boundary value problem. The solution of the original linear system is reduced to solving a collection of independent almost block diagonal linear systems which arise in orthogonal spline collocation applied to one-dimensional boundary value problems. The results of numerical experiments are presented which compare an implementation of the orthogonal spline collocation approach with a recently developed matrix decomposition code for solving finite element Galerkin equations.
Year
DOI
Venue
1995
10.1137/0916022
SIAM Journal on Scientific Computing
Keywords
Field
DocType
SEPARABLE ELLIPTIC PROBLEMS,PIECEWISE POLYNOMIAL SPACES,GAUSS POINTS,ORTHOGONAL SPLINE COLLOCATION,TENSOR PRODUCT,MATRIX DECOMPOSITION ALGORITHMS,GENERALIZED EIGENVALUE PROBLEM
Spline (mathematics),Boundary value problem,Mathematical optimization,Thin plate spline,Hermite spline,Mathematical analysis,Orthogonal collocation,Matrix decomposition,Collocation method,Mathematics,Elliptic curve
Journal
Volume
Issue
ISSN
16
2
1064-8275
Citations 
PageRank 
References 
4
0.54
8
Authors
2
Name
Order
Citations
PageRank
Bernard Bialecki111418.61
Graeme Fairweather216540.42