Spectral division methods for block generalized Schur decompositions

Author:

Sun Xiaobai,Quintana-Ortí Enrique

Abstract

We provide a different perspective of the spectral division methods for block generalized Schur decompositions of matrix pairs. The new approach exposes more algebraic structures of the successive matrix pairs in the spectral division iterations and reveals some potential computational difficulties. We present modified algorithms to reduce the arithmetic cost by nearly 50%, remove inconsistency in spectral subspace extraction from different sides (left and right), and improve the accuracy of subspaces. In application problems that only require a single-sided deflating subspace, our algorithms can be used to obtain a posteriori estimates on the backward accuracy of the computed subspaces with little extra cost.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference27 articles.

1. W. F. Arnold and A. J. Laub. Generalized eigenproblem algorithms and software for algebraic Riccati equations. Proc. IEEE, 72:1746–1754, 1984.

2. Using the matrix sign function to compute invariant subspaces;Bai, Zhaojun;SIAM J. Matrix Anal. Appl.,1998

3. An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems;Bai, Zhaojun;Numer. Math.,1997

4. The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers;Bai, Z.;SIAM J. Sci. Comput.,1997

5. P. Benner. Contributions to the Numerical Solution of Algebraic Riccati Equations and Related Eigenvalue Problems. Logos–Verlag, Berlin, Germany, 1997.

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