Formulas for bivariate hyperosculatory interpolation

Author:
Herbert E. Salzer

Journal:
Math. Comp. **25** (1971), 119-133

MSC:
Primary 65.20

DOI:
https://doi.org/10.1090/S0025-5718-1971-0287671-8

MathSciNet review:
0287671

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Abstract: For a given function , bivariate hyperosculatory interpolation formulas are obtained by employing a suitably constructed binary *n*ic that is fitted to the values of and its first and second partial derivatives at the *m* points of a rectangular Cartesian grid, where ( and are small integers . In terms of the variables (*p, q*), where (and ), we have . Often, for having a specified desirable form, this problem turns out to be insoluble for every configuration of the points . When this is not the case, it generally requires considerable investigation to find a practical configuration of points for which there is a solution of the form . Formulas are found for choices of , and soluble configurations of points , that have dominant remainder terms in

**[1]**H. E. Salzer & G. M. Kimbro,*Tables for Bivariate Osculatory Interpolation over a Cartesian Grid*, Convair Astronautics, 1958, 40 pp. Note especially the introductory text, by the present writer, on pp. 1-23. MR**0099106 (20:5550)****[2]**H. E. Salzer,*Some New Divided Difference Algorithms for Two Variables*, Proc. Sympos. Numerical Approximation (Madison, Wis., 1958), Univ. of Wisconsin Press, Madison, Wis., 1959, pp. 61-98. MR**21**#960. MR**0102166 (21:960)****[3]**H. E. Salzer, "Divided differences for functions of two variables for irregularly spaced arguments,"*Numer. Math.*, v. 6, 1964, pp. 68-77. MR**29**#2939. MR**0165659 (29:2939)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0287671-8

Keywords:
Bivariate hyperosculatory interpolation,
bivariate interpolation,
hyperosculatory interpolation,
Cartesian interpolation,
interpolation,
remainder formulas

Article copyright:
© Copyright 1971
American Mathematical Society