Multivariate Polynomial Interpolation to Traces on Manifolds

✍ Scribed by H.A. Hakopian; A.A. Sahakian

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 748 KB
• Volume: 80
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1995.1004

✦ Synopsis

A necessary and sufficient condition for polynomials defined on some (proper or improper) linear manifolds on (\mathbb{R}^{k}) is given in order that they agree there with the traces of a polynomial on (\mathbb{R}^{k}) (see H. A. Hakopian and A. A. Sahakian, in "Abstracts, International Workshop on Multivariate Interpolation and Approximation, Duisburg, 1989"). An inductive construction of this interpolating polynomial is obtained. The analogous interpolation on the sphere and with homogeneous polynomials is also presented, and some connections with other multivariate and finite element interpolations are explored. 1995 Academic Press, Inc.