On Numerical Analysis in Residue Number Systems
On Numerical Analysis in Residue Number Systems
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Date
1964
Authors
Lindamood, George Edward
Advisor
Rheinboldt, Werner C.
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Abstract
Recent attempts to utilize residue number systems
in digital computers have raised numerous questions about
adapting the techniques of numerical analysis to residue
number systems. Among these questions are the fundamental
problems of how to compare the magnitudes of two numbers, how
to detect additive and multiplicative overflow, and how to
divide in residue number systems. These three problems are
treated in separate chapters of this thesis and methods are
developed therein whereby magnitude comparison, overflow
detection, and division can be performed in residue number
systems. In an additional chapter, the division method is
extended to provide an algorithm for the direct approximation
of square roots in residue number systems. Numerous
examples are provided illustrating the nature of the problems considered and showing the use of the solutions presented in
practical computations. In a final chapter are presented the
results of extensive trial calculations for which a conventional
digital computer was programmed to simulate the use
of the division and square root algorithms in approximating
quotients and square roots in residue number systems. These
results indicate that, in practice, these division and
square root algorithms usually converge to the quotient or
square root somewhat faster than is suggested by the theory.