New Quasi-Newton Method for Solving Systems of Nonlinear Equations

0473663 - ÚI 2018 RIV CZ eng J - Journal Article
Lukšan, Ladislav - Vlček, Jan
New Quasi-Newton Method for Solving Systems of Nonlinear Equations.
Applications of Mathematics. Roč. 62, č. 2 (2017), s. 121-134. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : nonlinear equations * systems of equations * trust-region methods * quasi-Newton methods * adjoint Broyden methods * numerical algorithms * numerical experiments
OECD category: Applied mathematics
Impact factor: 0.897, year: 2017
http://hdl.handle.net/10338.dmlcz/146699

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.
Permanent Link: http://hdl.handle.net/11104/0270795