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• W1601375977 abstract "The floating-point implementation of a function on an interval often reduces to polynomial approximation, the polynomial being typically provided by Remez algorithm. However, the floating-point evaluation of a Remez polynomial sometimes leads to catastrophic cancellations. This happens when some of the polynomial coefficients are very small in magnitude with respects to others. In this case, it is better to force these coefficients to zero, which also reduces the operation count. This technique, classically used for odd or even functions, may be generalized to a much larger class of functions. An algorithm is presented that forces to zero the smaller coefficients of the initial polynomial thanks to a modified Remez algorithm targeting an incomplete monomial basis. One advantage of this technique is that it is purely numerical, the function being used as a numerical black box. This algorithm is implemented within a larger polynomial implementation tool that is demonstrated on a range of examples, resulting in polynomials with less coefficients than those obtained the usual way." @default.
• W1601375977 created "2016-06-24" @default.
• W1601375977 creator A5000711113 @default.
• W1601375977 creator A5035966925 @default.
• W1601375977 date "2008-03-04" @default.
• W1601375977 modified "2023-09-27" @default.
• W1601375977 title "Optimizing polynomials for floating-point implementation" @default.
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• W1601375977 hasPublicationYear "2008" @default.
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