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Mathematics of Computation

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Tabulation of constants for full grade $ I\sb{MN}$ approximants

Authors: V. Zakian and M. J. Edwards
Journal: Math. Comp. 32 (1978), 519-531
MSC: Primary 65A05
MathSciNet review: 0483277
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Abstract: For $ f:[0,\infty ) \to R$ the $ {I_{MN}}$ approximant of $ f(t)$ is

$\displaystyle {I_{MN}}(f,t) = \int_0^\infty {f(xt)\sum\limits_{i = 1}^N {{K_i}{e^{ - {\alpha _i}x}}dx,} } $

where $ {\alpha _i}$, $ {K_i}$ are defined constants. Under appropriate conditions on f, $ {I_{MN}}$ approximants of full grade are capable of giving good approximation both for small and large t. These and other properties of full grade $ {I_{MN}}$ approximants make them particularly useful in a wide range of practical applications. The constants $ {\alpha _i}$, $ {K_i}$ of full grade $ {I_{MN}}$ approximants are generated by partial fraction decompositions of certain Padé approximants to $ {e^{ - z}}$. The purpose of this paper is firstly to tabulate the constants $ {\alpha _i}$, $ {K_i}$ for all full grade $ {I_{MN}}$ approximants for $ 1 \leqslant N \leqslant 10$; secondly, to give accurate estimates of their precision; and thirdly, to describe the methods of tabulation and estimation in sufficient detail to allow the results of this paper to be extended readily.

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Article copyright: © Copyright 1978 American Mathematical Society