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- W4387298516 abstract "Our intpakX package extends the computer algebra system Maple. It allows, e.g., verified numerical calculations (computer-assisted proofs) built on arbitrary precision interval operations. Up to now, only the basic operations are supported in a guaranteed way. Concerning higher mathematical functions supported in Maple, there are no data about their accuracies available/published. Thus, it is not possible or at least very hard to build arbitrary precision interval functions using Maple’s intrinsic mathematical functions (nevertheless, intpakX offers such function implementations using some guard digits in an experimental way, which - of course - is not really a reliable mathematical approach). On the other hand there are software packages supporting reliable multiple precision interval functions like C-XSC, the MPFR and the MPFI libraries, and others. In the talk we discuss the features of some of these libraries in detail. We emphasize the different approaches (arbitrary precision arithmetic, staggered correction arithmetic, functions only for real arguments, functions for complex arguments, ...) and the most important resulting properties of the corresponding implementations. We also compare their performance and we comment on the actual integration of several of these libraries in C-XSC. The missing step is to bring together C-XSC and computer algebra packages like Maple and Mathematica. Combining fast verification methods and symbolic computations deeply extends the range of applications of rigorous mathematical methods." @default.
- W4387298516 created "2023-10-04" @default.
- W4387298516 creator A5083961677 @default.
- W4387298516 date "2010-12-15" @default.
- W4387298516 modified "2023-10-04" @default.
- W4387298516 title "VERIFICATION METHODS AND SYMBOLIC COMPUTATIONS" @default.
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- W4387298516 doi "https://doi.org/10.51286/albjm/1292178045" @default.
- W4387298516 hasPublicationYear "2010" @default.
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