Gauss harmonic interpolation formulas

  • Authors:

  • A. H. Stroud

  • Affiliations:

  • Texas A&M Univ., College Station

  • Venue:
  • Communications of the ACM
  • Year:
  • 1974

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Abstract

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.