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Existence of Gauss Harmonic Interpolation Formulas
David L. Barrow and A. H. Stroud
SIAM Journal on Numerical Analysis
Vol. 13, No. 1 (Mar., 1976), pp. 18-26
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2156462
Page Count: 9
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Let R be an open, bounded, simply connected region in the (x, y)-plane whose boundary is a rectifiable Jordan curve. Let (x*, y*) be an arbitrary point of R. We prove the existence of Gauss harmonic interpolation formulas for R and the point (x*, y*). Such formulas approximate a harmonic function at (x*, y*) in terms of a linear combination of its values at selected points on the boundary of R. These formulas are useful for approximating the solution of the Dirichlet problem for R.
SIAM Journal on Numerical Analysis © 1976 Society for Industrial and Applied Mathematics