Polynomial interpolation: Lagrange versus Newton
HTML articles powered by AMS MathViewer
- by Wilhelm Werner PDF
- Math. Comp. 43 (1984), 205-217 Request permission
Abstract:
We show that the Lagrangian form of the interpolating polynomial can be calculated with the same number of arithmetic operations as the Newtonian form.References
- T. P. Angelitch, G. Aumann, F. L. Bauer, R. Bulirsch, H. P. Künzi, H. Rutishauser, K. Samelson, R. Sauer, and J. Stoer, Mathematische Hilfsmittel des Ingenieurs. Teil III, Die Grundlehren der mathematischen Wissenschaften, Band 141, Springer-Verlag, Berlin-New York, 1968 (German). Herausgegeben von R. Sauer und I. Szabó; Unter Mitwirkung von H. Neuber, W. Nürnberg, K. Pöschl, E. Truckenbrodt und W. Zander. MR 0231562 P. J. Davis, Interpolation and Approximation, Blaisdell, Waltham, Mass., 1961.
- Peter Henrici, Essentials of numerical analysis with pocket calculator demonstrations, John Wiley & Sons, Inc., New York, 1982. MR 655251
- F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1956. MR 0075670
- Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
- Fred T. Krogh, Efficient algorithms for polynomial interpolation and numerical differentiation, Math. Comp. 24 (1970), 185–190. MR 258240, DOI 10.1090/S0025-5718-1970-0258240-X L. M. Milne-Thompson, The Calculus of Finite Differences, Macmillan, London, 1933. C. Schneider, Private communication.
- J. F. Steffensen, Interpolation, Chelsea Publishing Co., New York, N. Y., 1950. 2d ed. MR 0036799
- William J. Taylor, Method of Lagrangian curvilinear interpolation, J. Research Nat. Bur. Standards 35 (1945), 151–155. MR 0012920
- Wilhelm Werner, On the simultaneous determination of polynomial roots, Iterative solution of nonlinear systems of equations (Oberwolfach, 1982), Lecture Notes in Math., vol. 953, Springer, Berlin-New York, 1982, pp. 188–202. MR 678620
- Lonny B. Winrich, Note on a comparison of evaluation schemes for the interpolating polynomial, Comput. J. 12 (1969/70), 154–155. MR 242347, DOI 10.1093/comjnl/12.2.154
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Math. Comp. 43 (1984), 205-217
- MSC: Primary 65D05
- DOI: https://doi.org/10.1090/S0025-5718-1984-0744931-0
- MathSciNet review: 744931