An algorithm is described for reducing the generalized eigenvalue problem Ax = &lgr;Bx 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.
The full text of this article is premium content
No entries found
Log in to Read the Full Article
Please select one of the options below for access to premium content and features.
Create a Web Account
If you are already an ACM member, Communications subscriber, or Digital Library subscriber, please set up a web account to access premium content on this site.
Join the ACM
Become a member to take full advantage of ACM's outstanding computing information resources, networking opportunities, and other benefits.
Subscribe to Communications of the ACM Magazine
Get full access to 50+ years of CACM content and receive the print version of the magazine monthly.
Purchase the Article
Non-members can purchase this article or a copy of the magazine in which it appears.