an:04129893
Zbl 0689.65031
Pint??r, J.
Solving nonlinear equation systems via global partition and search: Some experimental results
EN
Computing 43, No. 4, 309-323 (1990).
00173001
1990
j
65H10 65K05 90C30
global optimization algorithm; Danilin-Piyavskij-Shubert algorithm; numerical tests; trigonometric systems; Shekel-type systems
The paper refers to a global optimization algorithm described by the author himself [Optimization 17, 187-202 (1986; Zbl 0595.90071)] which is a multivariate extension of the Danilin-Piyavskij-Shubert algorithm [cf. \textit{Yu. M. Danilin} and \textit{S. A. Piyavskij}, Theory of Optimal Solutions (Seminar, Kiev, 1967), No. 2, 25-37 (1967) and \textit{B. O. Shubert}, SIAM J. Numer. Anal. 9, 379-388 (1972; Zbl 0251.65052)]. In order to solve a system of nonlinear equations, \(F(x)=0\), it is transformed into a global optimization problem, \(\min f(x)\), where \(f(x)=\| F(x)\|\) with an appropriate norm \(\|\) \(\|\), such that the algorithm can be applied.
The paper's aim is to report about numerical tests performed with the algorithm. Two classes of problems are considered, i.e. trigonometric systems of equations and Shekel-type systems of equations where the coefficients involved were generated randomly.
H.Ratschek
Zbl 0595.90071; Zbl 0251.65052