Search

Through the introduction of multiple two parameter pairs of scaling factors, a modified formulation of the conjugate gradient scheme is derived. The individual pairs are separately assigned to the various substructure of a model so as to gauge the optimal local search direction and length. During the iteration process, this yields a successions of multiparameter dependent energy states. Seeking the appropriate minima, a vectorized multiparameter formulation of the conjugate gradient scheme is derived. Due to the manner of formulation, the scheme provides both global as well as substructural level orthogonality among successive iterates. To generalize the scheme, both pre and unpreconditioned versions are developed. Overall the methodology provides a potentially significant improvement in computational robustness. This is benchmarked in a series of numerical experiments.

The Unsymmetric Successive Overrelaxation (USSOR) iterative method is applied to the solution of the system of linear equationsA x=b, whereA is annxn nonsingular matrix. We find the values of the relaxation parameters ? and $$\bar \omega $$ for which the USSOR iterative method converges. Then we characterize those matrices which are equimodular toA and for which the USSOR iterative method converges.