Interval arithmetic block cyclic reduction on vector computers

Abstract

We introduce several algorithms for interval arithmetic block cyclic reduction for efficient application to vector computers under the condition that interval arithmetic inclusion properties be preserved. Interval arithmetic block cyclic reduction is used as part of almost globally convergent Newton-like methods for some classes of large nonlinear systems of equations. We further introduce truncated variants of the above algorithms and discuss their integration into nonlinear methods. We report numerical results carried out on a CRAY-1/M.