Multitasking algorithms on CRAY computers for interval arithmetic Newton-like methods for a class of systems of nonlinear equations

Abstract

For several classes of systems of nonlinear equations interval arithmetic methods can be defined which converge to a solution essentially under the condition that an initial inclusion is known, i.e. the convergence can be said to be global. We consider vector algorithms for an interval arithmetic Newton-like method which is combined with an interval arithmetic “fast solver” for nonlinear systems with block tridiagonal Jacobian. As an example we consider a nine point discretization of a twodimensional nonlinear Dirichlet problem. More specifically we discuss efficient algorithms for multiprocessor computers with two and four vector processors. The algorithms are intended to use all processors in parallel as far as possible under the condition that the vector efficiency in the parallel tasks does not substantially decrease. We report numerical results for programs using the multitasking routines on 1 and 2-processor CRAY-X/MP.