Accurate computation of divided differences of the exponential function
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- by A. McCurdy, K. C. Ng and B. N. Parlett PDF
- Math. Comp. 43 (1984), 501-528 Request permission
Abstract:
The traditional recurrence for the computation of exponential divided differences, along with a new method based on the properties of the exponential function, are studied in detail in this paper. Our results show that it is possible to combine these two methods to compute exponential divided differences accurately. A hybrid algorithm is presented for which our error bound grows quite slowly with the order of the divided difference.References
- Kendall E. Atkinson, An introduction to numerical analysis, John Wiley & Sons, New York-Chichester-Brisbane, 1978. MR 504339 S. D. Conte and C. de Boor, Elementary Numerical Analysis, 3rd ed., McGraw-Hill, New York, 1980.
- Chandler Davis, Explicit functional calculus, Linear Algebra Appl. 6 (1973), 193–199. MR 327792, DOI 10.1016/0024-3795(73)90019-0 G. F. Gabel, A Predictor-Corrector Method Using Divided Differences, Technical Report No. 5, Dept. of Computer Science, Univ. of Toronto, Oct. 1968. A. O. Gel’fand, Calculus of Finite Differences, Hindustan, India, 1971. W. Kahan & I. Farkas, "Algorithm 167—Calculation of confluent divided differences," Comm. ACM, v. 6, 1963, pp. 164-165. A. C. McCurdy, Accurate Computation of Divided Differences, UCB/ERL M80/28, Univ. of California, Berkeley, 1980.
- A. McCurdy, K. C. Ng, and B. N. Parlett, Accurate computation of divided differences of the exponential function, Math. Comp. 43 (1984), no. 168, 501–528. MR 758198, DOI 10.1090/S0025-5718-1984-0758198-0 K. C. Ng, The Computation of the Matrix Exponential, Thesis, Univ. of California, Berkeley, December 1983.
- G. Opitz, Steigungsmatrizen, Z. Angew. Math. Mech. 44 (1964), T52–T54 (German). MR 185806, DOI 10.1002/zamm.19640441321
- B. N. Parlett, A recurrence among the elements of functions of triangular matrices, Linear Algebra Appl. 14 (1976), no. 2, 117–121. MR 448846, DOI 10.1016/0024-3795(76)90018-5
- Robert C. Ward, Numerical computation of the matrix exponential with accuracy estimate, SIAM J. Numer. Anal. 14 (1977), no. 4, 600–610. MR 445806, DOI 10.1137/0714039
- L. M. Milne-Thomson, The Calculus of Finite Differences, Macmillan & Co., Ltd., London, 1951. MR 0043339
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 43 (1984), 501-528
- MSC: Primary 65D20; Secondary 33A10, 65G05
- DOI: https://doi.org/10.1090/S0025-5718-1984-0758198-0
- MathSciNet review: 758198