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The New qd Algorithms

Published online by Cambridge University Press:  07 November 2008

Beresford N. Parlett
Beresford N. Parlett
Affiliation:
Department of MathematicsUniversity of CaliforniaBerkeley CA 94720, USA, E-mail: parlett@math.berkeley.edu
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Extract

Let us think about ways to find both eigenvalues and eigenvectors of tridiagonal matrices. An important special case is the computation of singular values and singular vectors of bidiagonal matrices. The discussion is addressed both to specialists in matrix computation and to other scientists whose main interests lie elsewhere. The reason for hoping to communicate with two such diverse sets of readers at the same time is that the content of the survey, though of recent origin, is quite elementary and does not demand familiarity with much beyond triangular factorization and the Gram-Schmidt process for orthogonalizing a set of vectors. For some readers the survey will cover familiar territory but from a novel perspective. The justification for presenting these ideas is that they lead to new variations of current methods that run a lot faster while achieving greater accuracy.

Type
Research Article
Information
Acta Numerica , Volume 4 , January 1995 , pp. 459 - 491
Copyright
Copyright © Cambridge University Press 1995

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References

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