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UBC CS TR-93-39 Summary

Tridiagonalization Costs of the Bandwidth contraction and Rutistauser-Schwarz Algorithms, November 1993 Ian Cavers, 20 pages

In this paper we perform detailed complexity analyses of the Bandwidth Contraction and Rutishauser-Schwarz tridiagonalization algorithms using a general framework for the analysis of algorithms employing sequences of either standard or fast Givens transformations. Each algorithm's analysis predicts the number of flops required to reduce a generic densely banded symmetric matrix to tridiagonal form. The high accuracy of the analyses is demonstrated using novel symbolic sparse tridiagonalization tools, Xmatrix and Trisymb.

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