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On the simultaneous tridiagonalization of two symmetric matrices. (English) Zbl 1221.65107

Summary: We discuss congruence transformations aimed at simultaneously reducing a pair of symmetric matrices to tridiagonal-tridiagonal form under the very mild assumption that the matrix pencil is regular. We outline the general principles and propose a unified framework for the problem. This allows us to gain new insights, leading to an economical approach that only uses Gauss transformations and orthogonal Householder transformations. Numerical experiments show that the approach is numerically robust and competitive.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A22 Matrix pencils
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References:

[1] Garvey S.D., Tisseur F., Friswell M.I., Penny J.E.T., Prells U.: Simultaneous tridiagonalization of two symmetric matrices. Int. J. Numer. Meth. Eng. 57(12), 1643–1660 (2003) · Zbl 1043.65065
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[4] Tisseur F.: Tridiagonal–diagonal reduction of symmetric indefinite pairs. SIAM J. Matrix Anal. Appl. 26(1), 215–232 (2004) · Zbl 1079.65055
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