Incorporating origin shifts into the QR algorithm for symmetric tridiagonal matrices
- 1 June 1970
- journal article
- Published by Association for Computing Machinery (ACM) in Communications of the ACM
- Vol. 13 (6) , 365-367
- https://doi.org/10.1145/362384.362501
Abstract
The QR iteration for the eigenvalues of a symmetric tridiagonal matrix can be accelerated by incorporating a sequence of origin shifts. The origin shift may be either subtracted directly from the diagonal elements of the matrix or incorporated by means of an implicit algorithm. Both methods have drawbacks: the direct method can unnecessarily degrade small eigenvalues, while the implicit method can effectively loose the shift and thereby retard the convergence. This paper presents a new method which has neither drawback.Keywords
This publication has 4 references indexed in Scilit:
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- TheQR andQL algorithms for symmetric matricesNumerische Mathematik, 1968
- RationalQR transformation with Newton shift for symmetric tridiagonal matricesNumerische Mathematik, 1968
- The LLT and QR methods for symmetric tridiagonal matricesThe Computer Journal, 1963