Vandermonde with Arnoldi
Vandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem. This amounts to on-the-fly construction of discr...
| Main Authors: | , , |
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| 格式: | Journal article |
| 语言: | English |
| 出版: |
Society for Industrial and Applied Mathematics
2021
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| 总结: | Vandermonde matrices are exponentially ill-conditioned, rendering the familiar “polyval(polyfit)” algorithm for polynomial interpolation and least-squares fitting ineffective at higher degrees. We show that Arnoldi orthogonalization fixes the problem. This amounts to on-the-fly construction of discrete orthogonal polynomials by Stieltjes orthogonalization. |
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