| Abstract: | The paper contains a method for recovering a function from a table of its values. The method ensures smoothing of measured data, can be easily transformed into an algorithm and used in automatic information processing. The reconstruction method described in the paper is related to the approximation of smooth functions by means of some special splines, called S-splines, introduced by one of the authors. Conditions for stability and convergence of S-splines are obtained.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 10, pp. 197–206, 1984.The authors would like to thank Prof. V. M. Tikhomirov for advice and help with this work; thanks are also due to V. A. Gruzdev and E. V. Logacheva who provided their programs and computations. |
