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

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