Some approximate integration formulas of degree 3 for ann-dimensional simple

1966 ◽  
Vol 9 (1) ◽  
pp. 38-45 ◽  
Author(s):  
A. H. Stroud
Keyword(s):  
Integration Formulas ◽  
Approximate Integration

scholarly journals TOP EVALUATION FOR THE RA TION FOR THE RATE OF FUNC TE OF FUNCTIONAL OF ERROR AL OF ERROR WEIGHT CUBATURE FORMUL TURE FORMULA IN SP A IN SPACE

2019 ◽  
Vol 3 (4) ◽  
pp. 32-37
Author(s):  
Ozodjon Isomidinovich Jalolov ◽  
◽  
Khurshidzhon Usmanovich Khayatov
Keyword(s):  
Sobolev Space ◽  
Upper Bound ◽  
Cubature Formula ◽  
Integration Formulas ◽  
Error Functional ◽  
The Error Functional ◽  
Error Weight ◽  
Norm Of The Error ◽  
Approximate Integration

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

Best Approximate Integration Formulas

1950 ◽  
Vol 29 (1-4) ◽  
pp. 118-123 ◽  
Author(s):  
Leroy F. Meyers ◽  
Arthur Sard
Keyword(s):  
Integration Formulas ◽  
Approximate Integration

scholarly journals Algorithm for Calculating the Global Minimum of a Smooth Function of Several Variables

2021 ◽  
Vol 8 (4) ◽  
pp. 591-596
Author(s):  
Zhetkerbay Kaidassov ◽  
Zhailan S. Tutkusheva
Keyword(s):  
Global Minimum ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Computational Experiments ◽  
Quadrature Formulas ◽  
Cubature Formulas ◽  
Integration Formulas ◽  
C Programming ◽  
Approximate Integration

Every year the interest of theorists and practitioners in optimisation problems is growing, and extreme problems are found in all branches of science. Local optimisation problems are well studied and there are constructive methods for their solution. However, global optimisation problems do not meet the requirements in practice; therefore, the search for the global minimum remains one of the major challenges for computational and applied mathematics. This study discusses the search for the global minimum of multidimensional and multiextremal problems with high precision. Mechanical quadrature formulas, that is, the formulas for approximate integration were applied to calculate the integrals. Of all the approximate integration formulas, the Sobolev lattice cubature formulas with a regular boundary layer were chosen. In multidimensional examples, the Sobolev formulas are optimal. Computational experiments were carried out in the most popular C++ programming language. Based on the computational experiments, a new algorithm was proposed. In three-dimensional space, the calculations of the global minimum have been described using specific examples. Computational experiments show that the proposed algorithm works for multiextremal problems with the same amount of time as for convex ones.

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