期刊
LINEAR ALGEBRA AND ITS APPLICATIONS
卷 420, 期 1, 页码 86-101出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.laa.2006.06.028
关键词
quasiseparable matrices; Hessenberg form; tridiagonal form; QR iteration; eigenvalue computation
In this paper we design a fast new algorithm for reducing an N x N quasiseparable matrix to upper Hessenberg form via a sequence of N - 2 unitary transformations. The new reduction is especially useful when it is followed by the QR algorithm to obtain a complete set of eigenvalues of the original matrix. In particular, it is shown that in a number of cases some recently devised fast adaptations of the QR method for quasiseparable matrices can benefit from using the proposed reduction as a preprocessing step, yielding lower cost and a simplification of implementation. (c) 2006 Elsevier Inc. All rights reserved.
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