Brezinski, C.; Chehab, J.-P. Multiparameter iterative schemes for the solution of systems of linear and nonlinear equations. (English) Zbl 0949.65054 SIAM J. Sci. Comput. 20, No. 6, 2140-2159 (1999). 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. Reviewer: E.Allgower (Fort Collins) Cited in 9 Documents 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 Keywords:nonlinear systems; fixed point methods; convergence acceleration; hybrid procedure; Richardson extrapolation; algorithms; relaxation; steepest descent method; numerical examples; reaction-diffusion problems; bifurcations Software:na1 PDFBibTeX XMLCite \textit{C. Brezinski} and \textit{J. P. Chehab}, SIAM J. Sci. Comput. 20, No. 6, 2140--2159 (1999; Zbl 0949.65054) Full Text: DOI