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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)

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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