Tabulation of constants for full grade approximants
Authors:
V. Zakian and M. J. Edwards
Journal:
Math. Comp. 32 (1978), 519531
MSC:
Primary 65A05
MathSciNet review:
0483277
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Abstract: For the approximant of is where , are defined constants. Under appropriate conditions on f, approximants of full grade are capable of giving good approximation both for small and large t. These and other properties of full grade approximants make them particularly useful in a wide range of practical applications. The constants , of full grade approximants are generated by partial fraction decompositions of certain Padé approximants to . The purpose of this paper is firstly to tabulate the constants , for all full grade approximants for ; 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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 [1]
 E. B. DALE & I. A. FURZER, "An application of Zakian's method to solve the dynamics of a periodically cycled plate column," Chem. Eng. Sci., v. 29, 1974, pp. 23782380.
 [2]
 M. J. EDWARDS, "Applications of Zakian's and approximants to the unsteady state solution of the differential equations of a periodicallycycled plate column," Chem. Eng. J., v. 15, 1977, pp. 119125.
 [3]
 L. FOX & D. F. MAYERS, Computing Methods for Scientists and Engineers, Clarendon Press, Oxford, 1968. MR 0239715 (39:1072)
 [4]
 V. I. KRYLOV & N. S. SKOBLYA, Handbook of Numerical Inversion of Laplace Transforms, Israel Program for Scientific Translations, Jerusalem, 1969. MR 0391481 (52:12302)
 [5]
 Y. LUKE, The Special Functions and Their Approximations, Vol. 2, Academic Press, New York, 1969.
 [6]
 R. PIESSENS, "On a numerical method for the calculation of transient responses," J. Franklin Inst., v. 292, 1971, pp. 5764. MR 0323080 (48:1438)
 [7]
 A. J. RODRIGUES, "Properties of constants for a quadrature formula to evaluate Bromwich's integral," J. Inst. Math. Appl., v. 18, 1976, pp. 4956. MR 0413446 (54:1560)
 [8]
 E. B. SAFF & R. S. VARGA, "On the zeros and poles of Padé approximants to ," Numer. Math., v. 25, 1975, pp. 114. MR 0399429 (53:3273)
 [9]
 H. E. SALZER, "Orthogonal polynomials arising in the numerical evaluation of inverse Laplace transforms," MTAC, v. 9, 1955, pp. 164177. MR 0078498 (17:1203d)
 [10]
 H. E. SALZER, "Additional formulas and tables for orthogonal polynomials originating from inversion integrals," J. Mathematical Phys., v. 40, 1961, pp. 7286. MR 0129576 (23:B2612)
 [11]
 K. SINGHAL & J. VLACH, "Computation of time domain response by numerical inversion of the Laplace transform," J. Franklin Inst., v. 299, 1975, pp. 109126. MR 0375744 (51:11934)
 [12]
 A. H. STROUD & D. SECREST, Gaussian Quadrature Formulae, PrenticeHall, Englewood Cliffs, N. J., 1966. MR 0202312 (34:2185)
 [13]
 Y. WU, V. ZAKIAN & D. J. GRAVES, "Diffusion and reversible reaction in a sphere: a numerical study using approximants," Chem. Eng. Sci., v. 31, 1976, pp. 153162.
 [14]
 V. ZAKIAN, "Numerical inversion of Laplace transform," Electron. Lett., v. 5, 1969, pp. 120121. MR 0245178 (39:6490)
 [15]
 V. ZAKIAN, Solution of Ordinary Linear Differential Systems by Numerical Inversion of Laplace Transforms, Control Systems Centre Report No. 132, University of Manchester Institute of Science and Technology, 1971.
 [16]
 V. ZAKIAN, "Solution of homogeneous ordinary linear differential systems by numerical inversion of Laplace transforms," Electron. Lett., v. 7, 1971, pp. 546548. MR 0319377 (47:7921)
 [17]
 V. ZAKIAN & R. COLEMAN, "Numerical inversion of rational Laplace transforms," Electron Lett., v. 7, 1971, pp. 777778. MR 0319358 (47:7902)
 [18]
 V. ZAKIAN, "Properties of approximants," in Padé Approximants and Their Applications (P. R. GravesMorris, Editor), Academic Press, London, 1973. MR 0327351 (48:5693)
 [19]
 V. ZAKIAN, "Properties of and approximants and applications to numerical inversion of Laplace transforms and initial value problems," J. Math. Anal. Appl., v. 50, 1975, pp. 191222. MR 0371033 (51:7256)
 [20]
 V. ZAKIAN, "Application of approximants to numerical initial value problems in differentialalgebraic systems," J. Inst. Math. Appl., v. 15, 1975, pp. 267272. MR 0381322 (52:2219)
 [21]
 V. ZAKIAN & M. J. EDWARDS, Tabulation of Constants for Full Grade Approximants, Control Systems Centre Report No. 312, University of Manchester Institute of Science and Technology, 1976.
 [22]
 V. ZAKIAN & M. J. EDWARDS, Comments on and Approximants, Control Systems Centre Report No. 317, University of Manchester Institute of Science and Technology, 1976.
 [23]
 V. ZAKIAN & M. J. EDWARDS, Application of Approximants to InitialValue Problems in HighOrder Linear Constant Differential and DifferentialAlgebraic Systems, Control Systems Centre Report No. 318, University of Manchester Institute of Science and Technology, 1976.
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DOI:
http://dx.doi.org/10.1090/S00255718197804832772
PII:
S 00255718(1978)04832772
Article copyright:
© Copyright 1978
American Mathematical Society
