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Multiparameter iterative schemes for the solution of systems of linear and nonlinear equations. (English) Zbl 0949.65054

Multiparameter generalizations of the linear and nonlinear Richardon extrapolation are introduced. The new algorithms are based upon using an optimal matricial relaxation instead of the optimal scalar relaxation of the steepest descent method. From this approach it is possible to set construct multiparameter versions of the \(\Delta^k\) method for solving fixed point problems. Several numerical examples illustrate the implementation of the schemes. The examples deal with reaction-diffusion problems which exhibit bifurcations.

MSC:

65H10 Numerical computation of solutions to systems of equations
65F10 Iterative numerical methods for linear systems
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems

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