Frontiers of Mathematics in China >

2009 , Vol. 4 >Issue 2: 381 - 404

DOI: https://doi.org/10.1007/s11464-009-0013-9

RESEARCH ARTICLE

Error analysis of Padé iterations for computing matrix invariant subspaces

  • Zhenyue ZHANG ,
  • Rui HE
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  • Department of Mathematics, Zhejiang University, Hangzhou 310027, China

Received date: 21 Sep 2008

Accepted date: 10 Nov 2008

Published date: 05 Jun 2009

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

The method of Padématrix iteration is commonly used for computing matrix sign function and invariant subspaces of a real or complex matrix. In this paper, a detailed rounding error analysis is given for two classical schemes of the Padé matrix iteration, using basic matrix floating point arithmetics. Error estimations of computing invariant subspaces by the Padé sign iteration are also provided. Numerical experiments are given to show the numerical behaviors of the Pad´e iterations and the corresponding subspace computation.

Key words： Invariant subspace; matrix sign function; rounding error; Padéiteration; subspace approximation

Cite this article

Zhenyue ZHANG , Rui HE . Error analysis of Padé iterations for computing matrix invariant subspaces[J]. Frontiers of Mathematics in China, 2009 , 4(2) : 381 -404 . DOI: 10.1007/s11464-009-0013-9

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