MATH 590: Meshfree Methods - Chapter 6 - Applied Mathematics

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Interpolation with Multivariate PolynomialsRemarkA similar theorem was already proved in [Chung and Yao (1977)].Chui’s theorem can be generalized to R s by using hyperplanes. Theproof is constructed with the help of an additional induction on s.fasshauer@iit.edu MATH 590 – Chapter 6 10
Interpolation with Multivariate PolynomialsRemarkA similar theorem was already proved in [Chung and Yao (1977)].Chui’s theorem can be generalized to R s by using hyperplanes. Theproof is constructed with the help of an additional induction on s.RemarkFor later reference we note that (m − 1)-unisolvency of the pointsx 1 , . . . , x N is equivalent to the fact that the matrix P withP jl = p l (x j ), j = 1, . . . , N, l = 1, . . . , M,has full (column-)rank. For N = M = ( )m−1+sm−1 this is the polynomialinterpolation matrix.fasshauer@iit.edu MATH 590 – Chapter 6 10
Page 3 and 4: OutlineInterpolation with Multivari
Page 6 and 7: Interpolation with Multivariate Pol
Page 16 and 17: ProofInterpolation with Multivariat
Page 18 and 19: ProofInterpolation with Multivariat
Page 38 and 39: Example: Reproduction of Linear Fun
Page 54 and 55: Scattered Data Fitting w/ More Gene
Page 68 and 69: Almost Negative Definite Matrices a
Page 76 and 77:
Almost Negative Definite Matrices a
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
References IAppendixReferencesBuhma
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MATH 590: Meshfree Methods - Chapter 6 - Applied Mathematics

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