Newton's method for concave operators with resolvent positive derivatives in ordered Banach spaces

被引：28

作者：

Damm, T ^{[1
]}

Hinrichsen, D

机构：

[1] Tech Univ Munich, Zentrum Math, D-80333 Munich, Germany

[2] Univ Bremen, Inst Dynam Syst, D-28334 Bremen, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2003年 / 363卷

关键词：

Newton's method; positive operators; concave operators; Riccati equation;

D O I：

10.1016/S0024-3795(02)00328-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a non-local convergence result for Newton's method applied to a class of nonlinear equations in ordered real Banach spaces. The key tools in our approach are special notions of concavity and the spectral theory of resolvent positive operators. (C) 2002 Published by Elsevier Science Inc.

引用

页码：43 / 64

页数：22

共 27 条

[1] ARENDT W, 1987, P LOND MATH SOC, V54, P321
[2] ALGORITHM - SOLUTION OF MATRIX EQUATION AX+XB = C
BARTELS, RH
STEWART, GW
[J]. COMMUNICATIONS OF THE ACM, 1972, 15 (09) : 820 - &
[3] Berman A., 1989, NONNEGATIVE MATRICES
[4] Berman A., 1994, CLASSICS APPL MATH, DOI [10.1016/C2013-0-10361-3, 10.1137/1.9781611971262, DOI 10.1137/1.9781611971262]
[5] MONOTONICITY OF SPECTRAL-RADIUS FOR POSITIVE OPERATORS ON ORDERED BANACH-SPACES
BURLANDO, L
[J]. ARCHIV DER MATHEMATIK, 1991, 56 (01) : 49 - 57
[6] Coppel W. A., 1974, Bulletin of the Australian Mathematical Society, V10, P377, DOI 10.1017/S0004972700041071
[7] State-feedback H∞-type control of linear systems with time-varying parameter uncertainty
Damm, T
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 351 : 185 - 210
[8] Newton's method for a rational matrix equation occurring in stochastic control
Damm, T
Hinrichsen, D
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 332 : 81 - 109
[9] ELSNER L, 1970, ARCH RATION MECH AN, V36, P356
[10] Fischer A., 1998, VIETNAM J MATH, V26, P147

← 1 2 3 →