Accurate solutions of structured generalized Kronecker product linear systems

In this paper, we consider the generalized Kronecker product (GKP) linear system associated with a class of consecutive-rank-descending (CRD) matrices arising from bivariate interpolation problems. Relying on the sign sequences of CRD matrices, we show that the associated GKP linear system is accura...

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Bibliographic Details
Published in:Numerical algorithms Vol. 87; no. 2; pp. 797 - 818
Main Authors: Yang, Zhao, Huang, Rong, Zhu, Wei, Liu, Jianzhou
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2021
Springer Nature B.V
Subjects:
Accuracy
Algebra
Algorithms
Bivariate analysis
Computer Science
Eigenvalues
Interpolation
Linear algebra
Linear systems
Numeric Computing
Numerical Analysis
Original Paper
Sequences
Theory of Computation
Bivariate interpolation problems
Componentwise forward errors
Generalized Kronecker product linear systems
Generalized Vandermonde matrices
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we consider the generalized Kronecker product (GKP) linear system associated with a class of consecutive-rank-descending (CRD) matrices arising from bivariate interpolation problems. Relying on the sign sequences of CRD matrices, we show that the associated GKP linear system is accurately solved with an “ideal” componentwise forward error. In particular, a pleasantly small componentwise relative forward error is provided to illustrate that each component of the solution is computed to high relative accuracy. We then present the sign sequences of generalized Vandermonde matrices to show that the associated GKP linear system is accurately solved with the desired componentwise forward errors. Numerical experiments are performed to confirm the high relative accuracy.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00988-5