Optimum Acceleration Factors for Iterative Solutions of Linear and Non-Linear Systems.
Final rept. 1 Dec 84-30 Nov 85,
TEXAS UNIV AT AUSTIN DEPT OF AEROSPACE ENGINEERING AND ENGINEERING MECHANICS
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Two different approaches to the acceleration of iterative algorithms for the numerical solution of differential systems have been developed. General form of the non-linear minimal residual method has been analytically determined and numerically confirmed for solving linear and non-linear problems. The method was applied to multi-step algorithms for effectively determining optimal values of each of the acceleration parameters at each time step. It was found that both the rate of iterative convergence and the smoothness of the iterative convergence can be substantially augmented by the use of these multiple optimal acceleration parameters. The second approach involves a composite adaptive method which is based on variational techniques. An automatic procedure for determining splitting parameters needed in the iterative solution of large sparse linear systems was developed. It was then complemented with the generalized conjugate gradient acceleration procedures and successfully applied in the symmetric successive overrelaxation method and in the shifted incomplete Cholesky method.
- Theoretical Mathematics