Transfinite mean value interpolation in general dimension

Mean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative at the boundary; and the construction of a Hermite interpolant when normal derivative data is also available. In this paper we generalize these results to domains in arbitrary dimension. Math Subject Classification: 41A05, 65D05

• Type: Journal
• Year: 2010
• Where: JCAM
• Authors: Solveig Bruvoll, Michael S. Floater
• Keywords: JCAM 2010, Mean Value Interpolation, Normal Derivative, Normal Derivative Data