M. Razaz's research while affiliated with University of Birmingham and other places

Publications (5)

Article
A number of test procedures are presented for measuring the floating-point characteristics of a processor in a given computing environment. By using these procedures, accurate values can be assigned to the number representation and precision-dependent parameters such as the normalization base, number of digits in the mantissa, nominal decimal preci...
Article
A detailed analysis is given of the accumulation of errors which may occur in evaluating a polynomial approximation to a given function. Both backward recursion using untransformed Chebyshev expansions and the much faster nested multiplication using the transformed simple polynomial form are treated. Two types of arithmetic are dealt with covering...

Citations

... where we can expand g(x) in terms of Chebyshev polynomials, and use the fact that g will be even. Schonfelder and Razaz [8] showed, however, that such expansions can give rise to serious error amplification if the function g varies greatly in size, as we have with Lo. They recommend extracting an explicit exponential term which will absorb most of the function variation, leaving a more stable function to be expanded. ...
... Backward and forward error analysis for Horner's rule was ÿrst given by Wilkinson [18]. The behaviour of the evaluation of Chebyshev representations of a polynomial is studied in [1,5,7,12131416] where an error analysis is given for the evaluation of Chebyshev series by using the Clenshaw algorithm and variations of it. However, on the evaluation of ÿnite series of general orthogonal polynomials there are very few references. ...