Multiparameter Iterative Schemes for the Solution of Systems of Linear and Nonlinear Equations
Copyright policy )Multiparameter Iterative Schemes for the Solution of Systems of Linear and Nonlinear Equations
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.
- UNIVERSITE LILLE 1 France
Iterative numerical methods for linear systems, numerical examples, Richardson extrapolation, Numerical computation of solutions to systems of equations, fixed point methods, steepest descent method, algorithms, Numerical solution of nonlinear eigenvalue and eigenvector problems, relaxation, reaction-diffusion problems, convergence acceleration, nonlinear systems, bifurcations, hybrid procedure
Iterative numerical methods for linear systems, numerical examples, Richardson extrapolation, Numerical computation of solutions to systems of equations, fixed point methods, steepest descent method, algorithms, Numerical solution of nonlinear eigenvalue and eigenvector problems, relaxation, reaction-diffusion problems, convergence acceleration, nonlinear systems, bifurcations, hybrid procedure
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