A perturbation analysis for nonlinear selfadjoint operator equations

A.C.M. Ran; M.C.B. Reurings; L. Rodman

doi:10.1137/05062873

A perturbation analysis for nonlinear selfadjoint operator equations

A.C.M. Ran
, M.C.B. Reurings
, L. Rodman

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

Perturbation analysis, including perturbation bounds, is developed for nonlinear operator equations of the form X = Q ± A*F(X)A, under perturbations of the given operators Q (which is assumed to be positive definite) and A and of the given operator function F(X) which takes self-adjoint operator values. Stability of fixed points under suitable map perturbations serves as the main technical tool. More detailed analysis is provided in the particular cases where F(X) is a power map. © 2006 Society for Industrial and Applied Mathematics.

Original language	English
Pages (from-to)	89-104 (electronic)
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	28
Issue number	1
DOIs	https://doi.org/10.1137/05062873
Publication status	Published - 2006

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MR2218944

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10.1137/05062873

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title = "A perturbation analysis for nonlinear selfadjoint operator equations",

abstract = "Perturbation analysis, including perturbation bounds, is developed for nonlinear operator equations of the form X = Q ± A*F(X)A, under perturbations of the given operators Q (which is assumed to be positive definite) and A and of the given operator function F(X) which takes self-adjoint operator values. Stability of fixed points under suitable map perturbations serves as the main technical tool. More detailed analysis is provided in the particular cases where F(X) is a power map. {\textcopyright} 2006 Society for Industrial and Applied Mathematics.",

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AU - Ran, A.C.M.

AU - Reurings, M.C.B.

AU - Rodman, L.

N1 - MR2218944

PY - 2006

Y1 - 2006

N2 - Perturbation analysis, including perturbation bounds, is developed for nonlinear operator equations of the form X = Q ± A*F(X)A, under perturbations of the given operators Q (which is assumed to be positive definite) and A and of the given operator function F(X) which takes self-adjoint operator values. Stability of fixed points under suitable map perturbations serves as the main technical tool. More detailed analysis is provided in the particular cases where F(X) is a power map. © 2006 Society for Industrial and Applied Mathematics.

AB - Perturbation analysis, including perturbation bounds, is developed for nonlinear operator equations of the form X = Q ± A*F(X)A, under perturbations of the given operators Q (which is assumed to be positive definite) and A and of the given operator function F(X) which takes self-adjoint operator values. Stability of fixed points under suitable map perturbations serves as the main technical tool. More detailed analysis is provided in the particular cases where F(X) is a power map. © 2006 Society for Industrial and Applied Mathematics.

U2 - 10.1137/05062873

DO - 10.1137/05062873

M3 - Article

SN - 0895-4798

VL - 28

SP - 89-104 (electronic)

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

IS - 1

ER -

A perturbation analysis for nonlinear selfadjoint operator equations

Abstract

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