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Author Crawford, C. R.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Language English
Subject Keyword Generalized eigenvalues ♦ Symmetric band matrices
Abstract An algorithm is described for reducing the generalized eigenvalue problem Ax = λBx to an ordinary problem, in case A and B are symmetric band matrices with B positive definite. If n is the order of the matrix and m the bandwidth, the matrices A and B are partitioned into m-by-m blocks; and the algorithm is described in terms of these blocks. The algorithm reduces the generalized problem to an ordinary eigenvalue problem for a symmetric band matrix C whose bandwidth is the same as A and B. The algorithm is similar to those of Rutishauser and Schwartz for the reduction of symmetric matrices to band form. The calculation of C requires order n2m operation. The round-off error in the calculation of C is of the same order as the sum of the errors at each of the n/m steps of the algorithm, the latter errors being largely determined by the condition of B with respect to inversion.
Description Affiliation: The Univ. of Toronto, Clarkson, Ont., Canada (Crawford, C. R.)
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2005-08-01
Publisher Place New York
Journal Communications of the ACM (CACM)
Volume Number 16
Issue Number 1
Page Count 4
Starting Page 41
Ending Page 44

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Source: ACM Digital Library