C-polynomials for rational approximation to the exponential function. (English) Zbl 0299.65010


65D10 Numerical smoothing, curve fitting
41A20 Approximation by rational functions
Full Text: DOI EuDML


[1] Ahlfors, L. V.: Complex Analysis. McGraw-Hill, New York 1953 · Zbl 0052.07002
[2] Axelsson, O.: A class ofA-stable methods. BIT 9 (1965) pp. 185-199 · Zbl 0208.41504
[3] Blue, J. L., Gummel, H. K.: Rational Approximations to Matrix Exponential for Systems of Stiff Differential Equations. J. of Comp. Phy. V. 5, No. 1 (1970) pp. 70-83 · Zbl 0185.41204
[4] Chipman, F. H.: Numerical Solution of Initial Value Problems UsingA-stable Runge-Kutta Processes. Ph. D. Thesis, University of Waterloo, Waterloo, Ontario 1971 · Zbl 0265.65035
[5] Dahlquist, G. G.: A special stability problem for linear multistep methods. BIT V. 3 (1963), pp. 27-43 · Zbl 0123.11703
[6] Ehle, B. L.: On Padé Approximations to the Exponential Function andA-stable Methods for the Numerical Solution of Initial Value Problems. Ph. D. Thesis, University of Waterloo, Waterloo, Ontario 1969
[7] Lambert, J. D., Sigurdsson, S. T.: Multistep Methods with Variable Matrix Coefficients. SIAM J. Num. Anal. V. 9 (1972), pp. 715-733 · Zbl 0246.65024
[8] Lanczos, C.: Applied Analysis. Pitman, 1957 · Zbl 0111.12403
[9] Lawson, J. D.: Generalized Runge-Kutta processes for stable systems with large Lipschitz constants. SIAM J. Num. Anal. V. 4 (1967), pp. 372-380 · Zbl 0223.65030
[10] Lawson, J. D.: Order Constrained Chebyshev Rational Approximation. To appear · Zbl 0671.41008
[11] Liniger, W.: Global accuracy andA-stability of one- and two-step integration formulae for stiff ordinary differential equations. Conference on the Numerical Solution of Differential Equations. Springer-Verlag, Berlin, 1969, pp. 188-193
[12] Liniger, W., Willoughby, R. A.: Efficient integration methods for stiff ordinary differential equations. SIAM J. Num. Anal. V. 7 (1970), pp. 47-66 · Zbl 0187.11003
[13] Nørsett, S. P.: One-step Methods of Hermite Type for Numerical Integration of Stiff Systems. To appear in BIT · Zbl 0278.65078
[14] Padé, H.: Sur la Représentation Ápprochée d’une Function par des Fractions Rationelles. Thesis, Ann de l’Ec Nor, Vol. 9, No. 3 (1892)
[15] Rainville, F. D.: Special Functions. MacMillan Com. New York 1960 · Zbl 0092.06503
[16] Sigurdsson, S. T.: Multistep Methods with Variable Matrix Coefficients for Systems of Ordinary Differential Equations. Thesis, University of Dundee, Dundee · Zbl 0227.65045
[17] Silverman, R. A.: Introductory Complex Analysis. Prentice Hall Inc. 1967 · Zbl 0145.29804
[18] Cody, W. J., Meinardus, G., Varga, R. S.: Chebyshev Rational Approximations to exp (?x) on [0, ?? and applications to Heat-Conduction Problems. J. of Approx. Th. V. 2, (1969), pp. 50-65 · Zbl 0187.11602
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