Karimov feruz raimovich integrallarni taqribiy hisoblashda optimal kvadratur formulalar

Степень внедрения и экономическая эффективность: Диссертация носит теоретический характер. На практике для вычисления точных интегралов приходится решать множество задач. Но не всегда удается решить точные интегралы аналитически. Поэтому необходимо произвести приблизительный расчет.
Область применения: При интегрировании функций его можно использовать для решения интегральных уравнений, если функция задана в табличной форме.
ANNOTATION
Key words: Gauss, Chebishev, Eyler, Nyuton, quadratur, kubator, algorithm, interpolation, integral, Kroneker.
Subjects of research: Quadratic and cubic formulas, error function of the cubic formula, optimal interpolation formulas.
Purpose of work: Learning quadratic formulas, learning quadratic formulas, learning how to create algorithms and programs, learning how to build optimal interpolation quadratic formulas.
Methods of research: The methodological basis of the research was the basic methods of computational mathematics, generalized functions and their application, methods of construction of quadratic and cubic formulas, algorithms for finding the norm and extreme function for error function and construction of optimal interpolation formulas.
The results obtained and their novelty: Algorithms and programs for interpolation quadrature and cubature formulas were developed. The errors of these formulas were evaluated.
Practical value: The dissertation has a theoretical character. In practice, many problems have to calculate exact integrals. However, it is not always possible to solve exact integrals analytically. Therefore, it is necessary to make an approximate calculation. When integrating functions, if the function is given in tabular form, it can be used to solve integral equations.
Degree of embed and economic efficiency: The dissertation has a theoretical character. In practice, many problems have to calculate exact integrals. But it is not always possible to solve exact integrals analytically. Therefore, it is necessary to make an approximate calculation.