Formulas for bivariate hyperosculatory interpolation

Author:
Herbert E. Salzer

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

MSC:
Primary 65.20

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]**Herbert E. Salzer and Genevieve M. Kimbro,*Tables for bivariate osculatory interpolation over a Cartesian grid.*, Convair Division of General Dynamics Corporation, San Diego, Calif., 1958. MR**0099106****[2]**Herbert E. Salzer,*Some new divided difference algorithms for two variables*, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, pp. 61–98. MR**0102166****[3]**Herbert E. Salzer,*Divided differences for functions of two variables for irregularly spaced arguments*, Numer. Math.**6**(1964), 68–77. MR**0165659**

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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