Recursive algorithms for solving systems of nonlinear equations. (English) Zbl 0674.65026

A way of generalizing one-dimensional root-finding algorithms for nonlinear equation to the multidimensional case by means of recursion is described.
The paper deals with the exploitation of the abilities of the PASCAL language to express the true recursion and to define special nonnumerical types of data in such a way that the basic structure of the algorithms is simply described and easily understood. It is also shown how a failure of the root finding algorithm can be prevented. 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.
The above algorithm in its robust version is proved to converge and to find a root under very general (and sometimes unfavourable) conditions. In comparison with conventional methods, (Newton-Raphson iteration, iteration by components) it has some advantages: no need for calculating and inverting the Jacobi matrix, and for special means against divergence.
Reviewer: J.Hřebíček


65H10 Numerical computation of solutions to systems of equations
Full Text: EuDML


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