A parametric approximation. (English. Russian original) Zbl 0839.65012

Kuznetsov, E. B.; Shalashilin, V. I.

Comput. Math. Math. Phys. 34, No. 12, 1511-1520 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 12, 1757-1769 (1994).

The authors consider the problem of selecting the best parameter in methods of parametric interpolation and approximation. They give such a statement of the interpolation problem that can be examined from the point of view of the method of continuation of the solution with respect to a parameter, and the original parameter can be introduced as the continuation parameter. Further, the problem reduces to the solution of a Cauchy problem of a special kind. Some additional problems of parametric approximation are briefly discussed and numerical examples illustrating the advantages of the authors’ approach are presented.

Reviewer: V.V.Kobkov (Novosibirsk)

MSC:

65D15	Algorithms for approximation of functions
65D05	Numerical interpolation
65D07	Numerical computation using splines

Keywords:

parametric approximation; best parameter; parametric interpolation; continuation parameter; Cauchy problem; numerical examples