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Floating-point versus Symbolic Computations in theQD-algorithm

โœ Scribed by ANNIE CUYT

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
315 KB
Volume
24
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

The convergence of columns in the univariate qd-algorithm to reciprocals of polar singularities of meromorphic functions has often proved to be very useful. Any q-column corresponding to a "simple pole of isolated modulus" converges to the reciprocal of the corresponding pole. By performing an equivalence transformation of the underlying corresponding continued fraction and programming the new qd-like scheme so as to compute algebraic expressions, the difference in convergence behaviour between the "simple pole" case and the "equal modulus" pole case of the floating-point algorithm is eliminated.

๐Ÿ“œ SIMILAR VOLUMES

All possible computed results in correct
All possible computed results in correct floating-point summation
โœ M. Pichat ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 770 KB

On a computer, any entry or elementary operation has two legitimate results, one by default and one by excess. Thus, a given algebraic algorithm with a single result is able, when processed on a computer, to generate a large set of floating-point results, all representative of the exact algebraic re