1983 Reports

The Accurate Solution of Certain Continuous Problems Using Only Single Precision

Jankowski, Michal; Wozniakowski, Henryk

A typical approach for finding the approximate solution of a continuous problem is through discretization with meshsize h such that the truncation error goes to zero with h. The discretization problem is solved in floating point arithmetic. Rounding-errors spoil the theoretical convergence and the error may even tend to infinity. In this paper we present algorithms of moderate cost which use only single precision and which compute the approximate solution of the integration and elliptic equation problems with full accuracy. These algorithms are based on the modified Gill-Møller algorithm for summation of very many terms, iterative refinement of a linear system with a special algorithm for the computation of residuals in single precision and on a property of floating point subtraction of nearby numbers.