MATH 590: Meshfree Methods - Chapter 6 - Applied Mathematics

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Example: Reproduction of Linear Functions using Gaussian RBFsHow do we have to modify our existing MATLAB program for scattereddata interpolation to incorporate these modifications?Earlier we solvedAc = y,with A jk = e −ε2 ‖x j −x k ‖ 2 , j, k = 1, . . . , N, c = [c 1 , . . . , c N ] T , andy = [f (x 1 ), . . . , f (x N )] T .fasshauer@iit.edu MATH 590 – Chapter 6 18
Example: Reproduction of Linear Functions using Gaussian RBFsHow do we have to modify our existing MATLAB program for scattereddata interpolation to incorporate these modifications?Earlier we solvedAc = y,with A jk = e −ε2 ‖x j −x k ‖ 2 , j, k = 1, . . . , N, c = [c 1 , . . . , c N ] T , andy = [f (x 1 ), . . . , f (x N )] T .Now we have to solve the augmented system[ ] [ ] [ A P c yP T=O d 0], (1)where A, c, and y are as before, and P jl = p l (x j ), j = 1, . . . , N,l = 1, . . . , 3, with p 1 (x) = 1, p 2 (x) = x, and p 3 (x) = y. Moreover, 0 isa zero vector of length 3, and O is a zero matrix of size 3 × 3.fasshauer@iit.edu MATH 590 – Chapter 6 18
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 84 and 85: References IAppendixReferencesBuhma

MATH 590: Meshfree Methods - Chapter 6 - Applied Mathematics

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