Extremal properties of polynomials and splines. Based on the Russian edition 1992. (English) Zbl 0976.41008

Korneichuk, N. P.; Ligun, A. A.; Babenko, V. F.

Computational Mathematics and Analysis Series. Commack, NY: Nova Science Publishers, Inc. 433 p. (1996).

This book contains a coherent elucidation of the significant facts on extremal properties of polynomials and splines. In addition, new methods are presented for solving extremal problems of the function theory that permitted the authors to find general approaches to the investigation of the properties of polynomials as well as splines. The foundation of such approach are theorems of comparison for rearrangements of functions that helped not only to state the general ideological position extremal properties of polynomials and splines established earlier, but to also prove a series of new strict irregularities for them.
See also: Extremal properties of polynomials and splines (Russian) [“Naukova Dumka”, Kiev, (1992; Zbl 0853.41006]).

MSC:

41A15

Spline approximation