A control-theoretic approach to the design of zero finding numerical methods

被引：45

作者：

Bhaya, Amit ^{[1
]}

Kaszkurewicz, Eugenius ^{[1
]}

机构：

[1] Univ Fed Rio de Janeiro, COPPE, Dept Elect Engn, BR-21945970 Rio De Janeiro, Brazil

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2007年 / 52卷 / 06期

关键词：

conjugate gradient (CG) algorithm; control Lyapunov functions (CLFs); iterative methods; proportional-integral-derivative control; zero finding methods;

D O I：

10.1109/TAC.2007.899109

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 [计算机科学与技术];

摘要：

In this paper, it is shown how'standard iterative methods for solving linear and nonlinear equations can be designed from the point of view of control. Appropriate choices of control Lyapunov functions (CLFs) lead to both continuous and discrete-time versions of the Newton-Raphson and conjugate gradient algorithms as well as new variants.

引用

页码：1014 / 1026

页数：13

共 56 条

[1]

ALBER YI, 1971, DIFF EQUAT, V7, P1461

[2]

Ariyur K. B., 2003, REAL TIME OPTIMIZATI

[3]

STABILIZATION WITH RELAXED CONTROLS [J].

ARTSTEIN, Z .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (11) :1163-1173

[4]

DISTRIBUTED ASYNCHRONOUS COMPUTATION OF FIXED-POINTS [J].

BERTSEKAS, DP .

MATHEMATICAL PROGRAMMING, 1983, 27 (01) :107-120

[5]

Betts J.T., 2001, ADV DESIGN CONTROL

[6]

Steepest descent with momentum for quadratic functions is a version of the conjugate gradient method [J].

Bhaya, A ;

Kaszkurewicz, E .

NEURAL NETWORKS, 2004, 17 (01) :65-71

[7]

BHAYA A, 2006, ADV DESIGN CONTROL

[8]

BOGGS PT, 1976, MATH COMPUT, V30, P512, DOI 10.1090/S0025-5718-1976-0416018-3

[9]

Abundance, diversity, and community patterns of Isopoda (Crustacea) in the Weddell Sea and in the Bransfield Strait, Southern Ocean [J].

Brandt, A .

ANTARCTIC SCIENCE, 2004, 16 (01) :5-10

[10]

Dynamical systems and sequence transformations [J].

Brezinski, C .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (48) :10659-10669

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