Premium
Evaluating products of matrix pencils and collapsing matrix products
Author(s) -
Benner Peter,
Byers Ralph
Publication year - 2001
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.251
Subject(s) - mathematics , matrix (chemical analysis) , product (mathematics) , rounding , matrix multiplication , complex matrix , algebra over a field , pure mathematics , discrete mathematics , combinatorics , computer science , geometry , physics , materials science , quantum mechanics , composite material , quantum , operating system , chemistry , chromatography
This paper describes three numerical methods to collapse a formal product of p pairs of matrices $$P=\mathop{\prod}\limits_{k=0}^{p-1} E_{k}^{-1}A_{k}$$ down to the product of a single pair Ê −1 Â . In the setting of linear relations, the product formally extends to the case in which some of the E k 's are singular and it is impossible to explicitly form P as a single matrix. The methods differ in flop count, work space, and inherent parallelism. They have in common that they are immune to overflows and use no matrix inversions. A rounding error analysis shows that the special case of collapsing two pairs is numerically backward stable. Copyright © 2001 John Wiley & Sons, Ltd.