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New Quasi-Newton Method for Solving Systems of Nonlinear Equations

SYSNO ASEP	0473663
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	New Quasi-Newton Method for Solving Systems of Nonlinear Equations
Author(s)	Lukšan, Ladislav (UIVT-O)_{SAI, RID} Vlček, Jan (UIVT-O)_{SAI, RID, ORCID}
Source Title	Applications of Mathematics. - : Springer - ISSN 0862-7940 Roč. 62, č. 2 (2017), s. 121-134
Number of pages	14 s.
Language	eng - English
Country	CZ - Czech Republic
Keywords	nonlinear equations ; systems of equations ; trust-region methods ; quasi-Newton methods ; adjoint Broyden methods ; numerical algorithms ; numerical experiments
Subject RIV	BA - General Mathematics
OECD category	Applied mathematics
R&D Projects	GA13-06684S GA ČR - Czech Science Foundation (CSF)
Institutional support	UIVT-O - RVO:67985807
UT WOS	000411068700001
EID SCOPUS	85015619483
DOI	10.21136/AM.2017.0253-16
Annotation	We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n^2) arithmetic operations per iteration in contrast with the Newton method, which requires O(n^3) operations per iteration. Computational experiments confirm the high efficiency of the new method.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2018

Number of the records: 1