TL;DR
This paper demonstrates that Arnoldi orthogonalization effectively stabilizes computations involving Vandermonde matrices, which are traditionally ill-conditioned and problematic for polynomial interpolation and fitting.
Contribution
The paper introduces Arnoldi orthogonalization as a novel method to improve the numerical stability of Vandermonde matrix computations.
Findings
Arnoldi orthogonalization improves stability of Vandermonde matrices
It enables effective polynomial interpolation at higher degrees
Addresses exponential ill-conditioning issues
Abstract
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.
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