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Scientific reports of Bukhara State University

Abstract

An upper bound is obtained for the norm of the error functional of the weight cubature formula in the Sobolev space . The modern formulation of the problem of optimization of approximate integration formulas is to minimize the norm of the error functional of the formula on the selected normalized spaces. In these works, the problem of optimality with respect to some definite space is investigated. Most of the problems are considered in the Sobolev space.

First Page

32

Last Page

37

DOI

10.52297/2181-1466/2019/3/4/3

References

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5. Shodimetov X.M. Reshetchatie kvadraturnie i kubaturnie formuli v prostranstvax S.L.Soboleva. Doktorskaya dissertatsiya. - Tashkent: 2002. - 218 s.

6. Baxvalov N.S. Chislennie metodi. T.1. - M.: Nauka, 1973.

7. Teoriya kubaturnix formul i prilojeniya funktsionalnogo analiza k nekotorim zadacham matematicheskoy fiziki (Pod red. S.L.Soboleva). - Novosibirsk: Nauka, 1973. - 263 s.

8. Noskov M.V. O dekartovix proizvedeniyax kubaturnix formul i vichislitelnaya matematika.- Novosibirsk: Nauka, 1980. - S. 114 - 118.

9. Sobolev S.L. Nekotorie primeneniya funktsionalnogo analiza v matematicheskoy fizike.- M.: Nauka, 1988. - 333 s.

10. Jalolov O.I. Ob odnoy asimptoticheskoy optimalnoy kubaturnoy formule //Dokl. AN RUz. - Tashkent, 2011. - №1 . - S. 15-19.

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