On the Convergence Rate of a Newton-Like Method for Inverse Eigenvalue and Inverse Singular Value Problems

Raymond H. CHAN; Zheng-jian BAI

On the Convergence Rate of a Newton-Like Method for Inverse Eigenvalue and Inverse Singular Value Problems

Research output: Journal Publications › Journal Article (refereed) › peer-review

Abstract

In this paper, we first note that Method III in Friedland, Nocedal, and Overton [SIAM J. Numer. Anal., 24 (1987), pp. 634–667] may not converge quadratically in the quotient sense. Then, we show that the method is convergent quadratically under a weaker notion of convergence — the root convergence. We also extend our results to the algorithm given in Chu [SIAM J. Numer. Anal., 29 (1992), pp. 885–903] for inverse singular value problems.

Original language	English
Pages (from-to)	59-69
Number of pages	13
Journal	International Journal of Applied Mathematics
Volume	13
Issue number	1
Publication status	Published - 2003
Externally published	Yes

Cite this

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title = "On the Convergence Rate of a Newton-Like Method for Inverse Eigenvalue and Inverse Singular Value Problems",

abstract = "In this paper, we first note that Method III in Friedland, Nocedal, and Overton [SIAM J. Numer. Anal., 24 (1987), pp. 634–667] may not converge quadratically in the quotient sense. Then, we show that the method is convergent quadratically under a weaker notion of convergence — the root convergence. We also extend our results to the algorithm given in Chu [SIAM J. Numer. Anal., 29 (1992), pp. 885–903] for inverse singular value problems.",

author = "CHAN, \{Raymond H.\} and Zheng-jian BAI",

year = "2003",

language = "English",

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pages = "59--69",

journal = "International Journal of Applied Mathematics",

issn = "1311-1728",

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T1 - On the Convergence Rate of a Newton-Like Method for Inverse Eigenvalue and Inverse Singular Value Problems

AU - CHAN, Raymond H.

AU - BAI, Zheng-jian

PY - 2003

Y1 - 2003

N2 - In this paper, we first note that Method III in Friedland, Nocedal, and Overton [SIAM J. Numer. Anal., 24 (1987), pp. 634–667] may not converge quadratically in the quotient sense. Then, we show that the method is convergent quadratically under a weaker notion of convergence — the root convergence. We also extend our results to the algorithm given in Chu [SIAM J. Numer. Anal., 29 (1992), pp. 885–903] for inverse singular value problems.

AB - In this paper, we first note that Method III in Friedland, Nocedal, and Overton [SIAM J. Numer. Anal., 24 (1987), pp. 634–667] may not converge quadratically in the quotient sense. Then, we show that the method is convergent quadratically under a weaker notion of convergence — the root convergence. We also extend our results to the algorithm given in Chu [SIAM J. Numer. Anal., 29 (1992), pp. 885–903] for inverse singular value problems.

M3 - Journal Article (refereed)

SN - 1311-1728

VL - 13

SP - 59

EP - 69

JO - International Journal of Applied Mathematics

JF - International Journal of Applied Mathematics

IS - 1

ER -

On the Convergence Rate of a Newton-Like Method for Inverse Eigenvalue and Inverse Singular Value Problems

Abstract

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