NDLI: Numerical techniques for computing the inertia of products of matrices of rational numbers

Content Provider	ACM Digital Library
Author	May, John P. Saunders, B. David Wood, David Harlan
Abstract	Consider a rational matrix, particularly one whose entries have large numerators and denominators, but which is presented as a product of very sparse matrices with relatively small entries. We report on a numerical algorithm which computes the inertia of such a matrix in the nonsingular case and effectively exploits the product structure. We offer a symbolic/numeric hybrid algorithm for the singular case. We compare these methods with previous purely symbolic ones. By "purely symbolic" we refer to methods which restrict themselves to exact arithmetic and can assure that errors of approximation do not affect the results. Using an application in the study of Lie Groups as a plentiful source of examples of problems of this nature we explore the relative speeds of the numeric and hybrid methods as well as the range of applicability without error.
Starting Page	125
Ending Page	132
Page Count	8
File Format	PDF
ISBN	9781595937445
DOI	10.1145/1277500.1277520
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2007-07-25
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Lie group Symbolic/numeric hybrid method Matrix signature Product eigenvalue problem
Content Type	Text
Resource Type	Article

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Numerical techniques for computing the inertia of products of matrices of rational numbers