Lala B. Krishna

Some new results on Unsymmetric Successive Overrelaxation method

SummaryThe Unsymmetric Successive Overrelaxation (USSOR) iterative method is applied to the solution of the system of linear equationsAx=b, whereA is annxn nonsingular matrix. We find the values of the relaxation parameters ω and

Multiply Scaled Constrained Nonlinear Equation Solvers

\bar \omega

On the convergence of block constrained nonlinear equation solvers

for which the USSOR iterative method converges. Then we characterize those matrices which are equimodular toA and for which the USSOR iterative method converges.

Error Bounds for the SSOR Semi-Iterative Method

We obtain conditions for the convergence of SSOR and USSOR methods when the matrix A has a special form (so-called “red-black” ordering), using some vectorial norms. We give characterizations for the H-matrix with respect to the USSOR iteration matrix. Our results extend the work of Alefeld and Krishna.

Partitioned multiply scaled pseudo conjugate gradient schemes

To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

MULTIPLY SCALED CONSTRAINED NONLINEAR

Abstract The symmetric successive overrelaxation (SSOR) iterative method is applied to the solution of the system of linear equations A x = b , where A is an n×n nonsingular matrix. We give bounds for the spectral radius of the SSOR iterative matrix when A is an Hermitian positive definite matrix, and when A is a nonsingular M-matrix. Then, we discuss the convergence of the SSOR iterative method associated with a new splitting of the matrix A which extends the results of Varga and Buoni [1].

Multiply gauged solution initialization with steepest descent smoothing

The shortcomings associated with successive substitution nonlinear solvers are circumvented by introducing a so-called block constraint methodology. Specifically, by partitioning the governing field equations into various subsets, constraints can be applied individually to each separate block. To illustrate the formal properties of the scheme, a series of lemmas and a theorem will be developed. These define its convergence properties. Due to the generality of the approach taken, virtually any form of functional constraint may be employed.

Multiply gauged, mixed, progressively direct gradient based iterative solvers

The SSOR semi-iterative method is applied to the system of linear equations