Douglas M. Priest

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We present techniques which may be used to perform computations of very high accuracy using only straightforward oating point arithmetic operations of limited precision, and we prove the validity of these techniques under very general hypotheses satissed by most implementations of oating point arithmetic. To illustrate the application of these techniques,(More)
This document may not be reproduced or distributed in any form without the prior written permission of the author. All copies so authorized must bear this notice. Abstract Floating point arithmetics generally possess many regularity properties in addition to those that are typically used in roundoo error analyses; these properties can be exploited to(More)
We develop a simple method for scaling to avoid overflow and harmful underflow in complex division. The method guarantees that no overflow will occur unless at least one component of the quotient must overflow, otherwise the normwise error in the computed result is at most a few units in the last place. Moreover, the scaling requires only four floating(More)
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