Scattered data interpolation by linear combinations of translates of conditionally positive definite functions
- 1 January 1991
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 12 (1-2) , 137-152
- https://doi.org/10.1080/01630569108816421
Abstract
We study the problem of interpolating scattered data in Euclidean spaces by linear combinations of translates of conditionally positive definite functions. We show that certain symmetric linear combinations of these functions give rise to nonsingular interpolation matrices. We also estimate the norms of inverses of these matrices.Keywords
This publication has 6 references indexed in Scilit:
- Norm estimates for inverses of Euclidean distance matricesJournal of Approximation Theory, 1992
- Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matricesJournal of Approximation Theory, 1992
- On the matrix [¦xi − xj¦3] and the cubic spline continuity equationsJournal of Approximation Theory, 1987
- Interpolation of scattered data: Distance matrices and conditionally positive definite functionsConstructive Approximation, 1986
- Splines minimizing rotation-invariant semi-norms in Sobolev spacesPublished by Springer Nature ,1977
- On Certain Metric Spaces Arising From Euclidean Spaces by a Change of Metric and Their Imbedding in Hilbert SpaceAnnals of Mathematics, 1937