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The need for knowledge and reliability in numeric computation: Case study of multivariate Padé approximation. (English) Zbl 0799.65012
The authors review results of their theoretical and numerical investigations on the multivariate Padé approximation. They show how the knowledge about the problem environment can guide a number of choices needed before the computation. Secondly, they show how the defect correction algorithm adapted for interval arithmetic allows to improve numerical results. The computation of bivariate Padé approximation is illustrated in the case of the beta function.

65D15 Algorithms for approximation of functions
65D20 Computation of special functions and constants, construction of tables
65G30 Interval and finite arithmetic
41A21 Padé approximation
33B15 Gamma, beta and polygamma functions
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
Full Text: DOI
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