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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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SP Science China Press

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10.1007/978-981-287-396-5_5

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1869-1862

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Effective condition numbers and small sample stati

Authors: HuaiAn Diao XingHua Shi YiMin Wei
Publish Date: 2013/02/01
Volume: 56, Issue: 5, Pages: 967-982
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Abstract

In this paper we investigate the effective condition numbers for the generalized Sylvester equation AX − YB DX − YE = C F where A D ∈ ℝ m×m B E ∈ ℝ n×n and C F ∈ ℝ m×n We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation which requires Om 2 n + mn 2 flops comparing with Om 3 + n 3 flops for the generalized Schur and generalized HessenbergSchur methods for solving the generalized Sylvester equation Numerical examples illustrate the sharpness of our perturbation bounds

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