A way of generalizing onedimensional root-finding algorithms to the multidimensional case by means of recursion is shown and means to make the algorithms robust are discussed. In the second part, the algorithm is modified so as to exploit sparsity of large systems of equations for reducing the recursion depth and consequently decreasing the computational requirements of the method.
@article{104332,
author = {Ji\v r\'\i\ Jan},
title = {Recursive algorithms for solving systems of nonlinear equations},
journal = {Applications of Mathematics},
volume = {34},
year = {1989},
pages = {33-45},
zbl = {0674.65026},
mrnumber = {0982341},
language = {en},
url = {http://dml.mathdoc.fr/item/104332}
}
Jan, Jiří. Recursive algorithms for solving systems of nonlinear equations. Applications of Mathematics, Tome 34 (1989) pp. 33-45. http://gdmltest.u-ga.fr/item/104332/
Recursive method of numerical analysis of inertialess nonlinear circuits, (in Czech). Library of research and scientific writings, Technical University Brno, B-57, 1975. (1975)
Recursive method and general purpose program RANG to analyze nonlinear circuits, (in Czech). Research report, project no. III-3-1/1, Technical University Brno, 1975. (1975)
Analysis of nonlinear circuits by means of the generalized recursive method, Proc. of the II-nd Int. Conference on Electronic Circuits, Prague 1976. (1976)
Use of the recursive method in analysis of transients in nonlinear circuits, (in Czech). Thesis, Dept. of Computers, Technical University of Brno, 1976. (1976)
Recursive analysis of nonlinear circuits, (in Czech). Slaboproudý obzor 39, 1978, no. 1. (1978)
Recursive algorithms to solve systems of nonlinear equations, Proc. of the 7-th European Conference on Circuit Theory and Design, Prague 1985. (1985) | Zbl 0585.65041