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Mathematics of Computation

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Spectral division methods for block generalized Schur decompositions

Authors: Xiaobai Sun and Enrique S. Quintana-Ortí
Journal: Math. Comp. 73 (2004), 1827-1847
MSC (2000): Primary 65F15; Secondary 15A18, 15A22
Published electronically: May 11, 2004
MathSciNet review: 2059738
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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.

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Additional Information

Xiaobai Sun
Affiliation: Department of Computer Science, Duke University, D107, Levine Science Research Center, Durham, North Carolina 27708-0129

Enrique S. Quintana-Ortí
Affiliation: Departmento de Ingeniería y Ciencia de Computadores, Universidad Jaime I, 12080 Castellón, Spain

Keywords: Generalized eigenproblem, matrix sign and disc functions, spectral divide-and-conquer algorithms
Received by editor(s): August 13, 2002
Published electronically: May 11, 2004
Article copyright: © Copyright 2004 American Mathematical Society