Vol. 1, No. 1, 2006

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On interpolation and integration in finite-dimensional spaces of bounded functions

Per-Gunnar Martinsson, Vladimir Rokhlin and Mark Tygert

Vol. 1 (2006), No. 1, 133–142
Abstract

We observe that, under very mild conditions, an n-dimensional space of functions (with a finite n) admits numerically stable n-point interpolation and integration formulae. The proof relies entirely on linear algebra, and is virtually independent of the domain and of the functions to be interpolated.

Keywords
interpolation, numerical integration, quadrature
Mathematical Subject Classification 2000
Primary: 65-02
Milestones
Received: 10 December 2005
Accepted: 13 March 2006
Published: 9 May 2007
Authors
Per-Gunnar Martinsson
Department of Applied Mathematics
University of Colorado
526 UCB
Boulder, CO 80309
United States
Vladimir Rokhlin
Departments of Computer Science, Mathematics, and Physics
Yale University
New Haven, CT 06511
United States
Mark Tygert
Department of Mathematics
Yale University
New Haven, CT 06511
United States