Article ID Journal Published Year Pages File Type
4603099 Linear Algebra and its Applications 2008 12 Pages PDF
Abstract

Interpolation of smooth functions and the discretization of elliptic PDEs by means of radial functions lead to structured linear systems which, for equidistant grid points, have almost the (block) Toeplitz structure. We prove upper bounds for the condition numbers of the n×n Toeplitz matrices which discretize the model problem u″(x)=f(x), x∈(0,1), u(0)=a, u(1)=b over an equally spaced grid of n+2 points in [0,1] by means of the collocation method based on radial functions of the multiquadric, inverse multiquadric and Gaussian type. These bounds are asymptotically sharp.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory