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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:
- Scattered data interpolation
- Linear combinations
- Conditionally positive definite functions
- Distributions
- Fourier transform
- 1980 Mathematics subject classifications: Primary 41A05
- 1980 Mathematics subject classifications: Primary 41A63
- 1980 Mathematics subject classifications: Secondary 65D05
- 1980 Mathematics subject classifications: Secondary 41A30