Sequential and parallel synchronous alternating iterative methods

The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent.

On Newton-iterative methods for the solution of systems of nonlinear equations /

Based on the author's thesis, Yale.

Iterative and direct methods for solving Poisson's equation and their adaptability to ILLIAC IV,

Includes bibliography.

Reconstruction of a stationary flow from boundary data using iterative methods

In this paper, three iterative procedures (Landweber-Fridman, conjugate gradient and minimal error methods) for obtaining a stable solution to the Cauchy problem in slow viscous flows are presented and compared. A section is devoted to the numerical investigations of these algorithms. There, we use the boundary element method together with efficient stopping criteria for ceasing the iteration process in order to obtain stable solutions.

Iterative Methods for Equality-Constrained Least Squares Problems

We consider the linear equality-constrained least squares problem (LSE) of minimizing ${\|c - Gx\|}_2 $, subject to the constraint $Ex = p$. A preconditioned conjugate gradient method is applied to the Kuhn–Tucker equations associated with the LSE problem. We show that our method is well suited for structural optimization problems in reliability analysis and optimal design. Numerical tests are performed on an Alliant FX/8 multiprocessor and a Cray-X-MP using some practical structural analysis data.

Iterative and Pade solutions for the water-wave dispersion relation /

"April 1985."