Geodesic
About the Retrofit of the Valle'e–Poussin's Algorithm for Approximations of Multivalued Mappings by Algebraic Polynomial with Type Constraint Equality
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 526-532 
I. Yu. Vygodchikova. About the Retrofit of the Valle'e–Poussin's Algorithm for Approximations of Multivalued Mappings by Algebraic Polynomial with Type Constraint Equality. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 14 (2014) no. 4, pp. 526-532. http://geodesic.mathdoc.fr/item/ISU_2014_14_4_a5/
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     title = {About the {Retrofit} of the {Valle'e{\textendash}Poussin's} {Algorithm} for {Approximations} of {Multivalued} {Mappings} by {Algebraic} {Polynomial} with {Type} {Constraint} {Equality}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The discrete approximation of noisy data by algebraic polynomial with restriction of type equality is studied. The aim of the investigation is to obtain the fundamental properties of solution of the problem and development by them the new algorithm, more effective, in comparison with existing methods of the solution. The tasks of the research — gets the properties of the solution of the problem, presentation of the algorithm and the demonstration of its implementation. Research methodology continues P. L. Chebyshjov's and Valle–Pussen's method. Results. The criterion for optimality of the solution, which is a retrofit of the well-known in the theory of approximations of alternance P. L. Chebyshjov. Developed a rational algorithm, similar to the algorithm Vallee–Poussin. The conclusions. This problem has application to assess noise events at approximation to complex chaotic processes.

[1] Vygodchikova I. Yu., “On the uniqueness of the solution of problems in the best approximation of multivalued mappings algebraic polynomial”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 6:1–2 (2006), 11–19 (in Russian) | MR

[2] Zuhovickij S. I., Avdeeva L. I., Linear and convex programming, Nauka, M., 1967, 460 pp. (in Russian) | MR

[3] Vygodchikova I. Yu., “On the method of approximation of multivalued display algebraic polynomial”, Vestnic SSTU, Ser.: Math. Mech., 2013, no. 2(70), 7–12 (in Russian)

[4] Vygodchikova I. Yu., “About conditional task best the segment approximation of functions by algebraic polynomial”, Mathematics. Mechanics, 10, Saratov Univ. Press, Saratov, 2008, 12–15 (in Russian) | MR | Zbl

[5] Dem'janov V. F., Malozemov V. N., Introduction to minimax, Nauka, M., 1972, 368 pp. (in Russian) | MR

[6] Vygodchikova I. Yu., “About the monotone algorithm for solving task segment approximation of functions by algebraic polynomial with restriction”, Mathematics. Mechanics, 14, Saratov Univ. Press, Saratov, 2012, 20–23 (in Russian) | Zbl