Kramer, W.; Kulisch, U.; Lohner, R.: Numerical Toolbox for Verified Computing II: Theory, Algorithms and Pascal-XSC Programs. (Vol. I see [Ham93, Ham95]) Springer--Verlag, Berlin / Heidelberg / New York, to appear 1996. 40 K... Authors Home/Search Document Not in Database Summary Related Articles Check |
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Literature on Enclosure Methods and Related Topics - Gerd Bohlender (1996) (Correct)
.... were minisymposia on the subject at the yearly GAMM conferences (proceedings in ZAMM) at the IMACS conferences in Oslo [Rus86, Wah85] and Dublin [Bre92, Vic91] and talks at many ARITH meetings [ARITH] Related collections of research papers: Ada93, Alb93] Collected algorithms: Ham93, Ham95, Kra96] ffl Computer arithmetic for verification methods (interval operations, exact dot product) introduction [Loh92a, Hof93, Wol90a, Mei87] foundations [Kul75, Kul76, Kul76a, Kul77, Kul77a, Kul81, Kul83a, Kul84] software implementation [Apo67, Wip68, Boh78, Gru79, Gru80, Boh82, Boh82a, Boh83, ....
Kramer, W.; Kulisch, U.; Lohner, R.: Numerical Toolbox for Verified Computing II: Theory, Algorithms and Pascal-XSC Programs. (Vol. I see [Ham93, Ham95]) Springer--Verlag, Berlin / Heidelberg / New York, to appear 1996. 40 K... Authors
The Fifth Floating-Point Operation for Top-Performance Computers.. - Kulisch (1997) (1 citation) Self-citation (Kulisch) (Correct)
....via integer arithmetic. In combination with interval arithmetic, algorithms for numerous numerical problems were developed in short time by which computers could prove both existence and uniqueness of the computed solution, as well as deliver bounds for the solution with high accuracy [9] 10] [18]. It turns out that many iterative methods reach the desired accuracy faster if all dot products are evaluated in infinite precision arithmetic to full accuracy or with only one final rounding [23] 25] 26] Nevertheless, till today there is no commercial VLSI coprocessor available for the ....
....This increases the run time only marginally. By interval arithmetic and the optimal dot product modern numerical analysis has got new tools which allow new solution methods for numerical problems. Examples: The new methods for global optimization and for automatic differentiation [1] 9] 10] [18]. For the reverse mode of automatic differentiation, the memory overhead and the spatial complexity can be significantly reduced by the optimal dot product. There the dot product is considered as a single basic operation in the vector spaces [28] Often these tools allow a productive forward ....
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Kramer, W., Kulisch, U., Lohner, R.: Numerical Toolbox for Verified Computing II: Theory, Algorithms and PASCAL-XSC Programs, Springer, Berlin, 1996.
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