Paper Info
Title
Vandermonde With Arnoldi
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. This amounts to on-the-fly construction of discrete orthogonal polynomials by Stieltjes orthogonalization.
Year
DOI
Venue
2021
10.1137/19M130100X
SIAM REVIEW
Keywords
DocType
Volume
interpolation, least-squares, Vandermonde matrix, Arnoldi, polyval, polyfit, Fourier extension
Journal
63
Issue
ISSN
Citations 
2
0036-1445
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Brubeck Pablo D.100.34
Yuji Nakatsukasa29717.74
Lloyd N. Trefethen31024203.66