Browse Theses

A simple analytical unified approach is described for error detection and correction in numerical computations. The computation process may be implemented by a computer program or memory or by a specialized digital or analog device. This approach does not depend on the form of representation or on the specific features of the implementation of a program or a device computing the given function and is based on algebraic concepts, such as transcendental degree of field extensions. In particular, it was proved that, for a very broad class of functions, an algebraic equation can be written which related to each other the values of the function at a given point and at a few other points. This result is a generalization of the classical "addition theorem" of the algebraic theory of functions. The described approach results in a substantial reduction of the hardware overhead required for multiple error detection and correction, as compared to the check sum approach and to other methods previously known. ftn*All degree requirements completed in 1992, but degree will be granted in 1993.