Tabulation of constants for full grade $I_{MN}$ approximants
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- by V. Zakian and M. J. Edwards PDF
- Math. Comp. 32 (1978), 519-531 Request permission
Abstract:
For $f:[0,\infty ) \to R$ the ${I_{MN}}$ approximant of $f(t)$ is \[ {I_{MN}}(f,t) = \int _0^\infty {f(xt)\sum \limits _{i = 1}^N {{K_i}{e^{ - {\alpha _i}x}}dx,} } \] 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.References
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Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 519-531
- MSC: Primary 65A05
- DOI: https://doi.org/10.1090/S0025-5718-1978-0483277-2
- MathSciNet review: 0483277