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Communications of the ACM

Communications of the ACM

Gauss harmonic interpolation formulas

Let R be an open, bounded, simply connected region in the (x,y)-plane and let (x*,y*) be a point in R. Assuming R is starlike with respect to (x*,y*), we discuss a method for computing 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 certain selected points on the boundary of R. Such formulas are useful for approximating the solution of the Dirichlet problem for R.

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