Generalized recursive multivariate interpolation
HTML articles powered by AMS MathViewer
- by Earl H. McKinney PDF
- Math. Comp. 26 (1972), 723-735 Request permission
Abstract:
A generalized recursive interpolation technique for a set of linear functionals over a set of general univariate basis functions has been previously developed. This paper extends these results to restricted multivariate interpolation over a set of general multivariate basis functions. When the data array is a suitable configuration (e.g., an $n$-dimensional simplex), minimal degree multivariate interpolating polynomials are produced by this recursive interpolation scheme. By using product rules, recursive univariate interpolation applied to each variable singly produces multivariate interpolating polynomials (not of minimal degree) when the data are arranged in a hyper-rectangular array. By proper ordering of points in a data array, multivariate polynomial interpolation is accomplished over other arrays such as diamonds and truncated diamonds in two dimensions and their counterparts in $n$ dimensions.References
-
P. L. Walker, Generalized Recursive Interpolation, Thesis, University of Kansas, Lawrence, Kan., 1964. (Unpublished.)
H. C. Thacher, Jr., Inductive Interpolation Algorithm, 1963. (Unpublished.)
- A. C. R. Newbery, Interpolation by algebraic and trigonometric polynomials, Math. Comp. 20 (1966), 597–599. MR 203905, DOI 10.1090/S0025-5718-1966-0203905-8 W. E. Milne, W. Arntzen, N. Reynolds & J. Wheelock, Mathematics for Digital Computers. Vol. I. Multivariate Interpolation, WADC Technical Report 57-556, 1958.
- Martin Davis, Computability and unsolvability, McGraw-Hill Series in Information Processing and Computers, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR 0124208
- J. F. Steffensen, Interpolation, Chelsea Publishing Co., New York, N. Y., 1950. 2d ed. MR 0036799
- W. M. Kincaid, Note on the error in interpolation of a function of two independent variables, Ann. Math. Statistics 19 (1948), 85–88. MR 24231, DOI 10.1214/aoms/1177730295
- Arthur Sard, Remainders: functions of several variables, Acta Math. 84 (1951), 319–346. MR 40354, DOI 10.1007/BF02414860
- Henry C. Thacher Jr., Derivation of interpolation formulas in several independent variables, Ann. New York Acad. Sci. 86 (1960), 758–775 (1960). MR 116456
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 723-735
- MSC: Primary 65D05; Secondary 41A63
- DOI: https://doi.org/10.1090/S0025-5718-1972-0341797-X
- MathSciNet review: 0341797