By R. Baker Kearfott, John Pryce, Nathalie Revol (auth.), Annie Cuyt, Walter Krämer, Wolfram Luther, Peter Markstein (eds.)
This ebook constitutes the completely refereed post-proceedings of the Dagstuhl Seminar 08021 on Numerical Validation in present Architectures held at Dagstuhl fortress, Germany, in January 2008.
The sixteen revised complete papers offered have been chosen in the course of rounds of reviewing and enhancements. The papers are prepared in topical sections on languages, software program structures and instruments, new verification ideas in response to period mathematics, purposes in technological know-how and engineering, and novel ways to verification.
Read Online or Download Numerical Validation in Current Hardware Architectures: International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 6-11, 2008. Revised Papers PDF
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Extra info for Numerical Validation in Current Hardware Architectures: International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 6-11, 2008. Revised Papers
Computing x·y for floating point vectors x, and y in C-XSC results in the best possible floating point result (exact mathematical result rounded to the nearest floating point number; correctly rounded result). Using the C-XSC data type dotprecision (so called long accumulator), the user can even store the result of dot products of floating point vectors with even quintillions of components errorfree. Let us introduce staggered numbers in a more formal way [6,27,36]. An ordinary staggered interval number x is given by n−1 n−1 xi + [xn , xn+1 ] = x := i=1 xi + X.
037. Needless to say that the eﬀortless but appropriate choice of the tail tN has greatly improved the accuracy of the result, from 27 to 40 signiﬁcant digits! 5 Future Work The project is an ongoing project and future work includes the inventory and symbolic implementation of representations for the Coulomb wave functions, the Legendre functions, the Riemann zeta function and other frequently used special functions. As they become available, the list of functions available in the tabulate (Sect.
Classical convergence results are given, formulated in terms of element and value regions. The connection with Pad´e approximants, two-point Pad´e approximants, moment problems, Stieltjes integral transform representations and orthogonal polynomials are discussed. In Part II the reader is oﬀered algorithms to construct various continued fraction representations of functions, known either by one or more (formal) series representations or by a set of function values. When evaluating a continued fraction representation, only a ﬁnite part of the fraction can be taken into account.
Numerical Validation in Current Hardware Architectures: International Dagstuhl Seminar, Dagstuhl Castle, Germany, January 6-11, 2008. Revised Papers by R. Baker Kearfott, John Pryce, Nathalie Revol (auth.), Annie Cuyt, Walter Krämer, Wolfram Luther, Peter Markstein (eds.)