Fast inversion of vandermonde-like matrices involving orthogonal polynomials |
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Authors: | D Calvetti L Reichel |
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Institution: | (1) Department of Pure and Applied Mathematics, Stevens Institute of Technology, 07030 Hoboken, NJ;(2) Department of Mathematics and Computer Science, Kent State University, 44242 Kent, OH |
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Abstract: | Let {q}
j
=0n–1
be a family of polynomials that satisfy a three-term recurrence relation and let {t
k
}
k
=1n
be a set of distinct nodes. Define the Vandermonde-like matrixW
n
=w
jk
]
k,j
=1n
,w
jk
=q
j–1(t
k
). We describe a fast algorithm for computing the elements of the inverse ofW
n
inO(n
2) arithmetic operations. Our algorithm generalizes a scheme presented by Traub 22] for fast inversion of Vandermonde matrices. Numerical examples show that our scheme often yields higher accuracy than the LINPACK subroutine SGEDI for inverting a general matrix. SGEDI uses Gaussian elimination with partial pivoting and requiresO(n
3) arithmetic operations.Dedicated to Gene H. Golub on his 60th birthdayResearch supported by NSF grant DMS-9002884. |
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Keywords: | 65F05 65D05 65D30 |
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