Error analysis of Padé iterations for computing matrix invariant subspaces

Zhenyue Zhang; Rui He

doi:10.1007/s11464-009-0013-9

Front. Math. China ›› 2009, Vol. 4 ›› Issue (2) : 381 -404. DOI: 10.1007/s11464-009-0013-9

Research Article

RESEARCH ARTICLE

Error analysis of Padé iterations for computing matrix invariant subspaces

Zhenyue Zhang ¹^,^a
, Rui He ¹

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Abstract

The method of Padé matrix 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 Pad’e 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 Padé iterations and the corresponding subspace computation.

Keywords

Invariant subspace / matrix sign function / rounding error / Padé iteration / subspace approximation

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Zhenyue Zhang, Rui He. Error analysis of Padé iterations for computing matrix invariant subspaces. Front. Math. China, 2009, 4(2): 381-404 DOI:10.1007/s11464-009-0013-9

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