Integro-Differential Polynomial and Trigonometrical Splines and Quadrature Formulas

Результат исследований: Научные публикации в периодических изданияхстатья

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Abstract: This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following: the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed as the sum of products of the basic splines and the values of function in nodes and/or the values of its derivatives and/or the values of integrals of this function over subintervals. Basic splines are determined by using a solving system of equations which are provided by the set of functions. It is known that when integrals of the function over the intervals is equal to the integrals of the approximation of the function over the intervals then the approximation has some physical parallel. The splines which are constructed here satisfy the property of the fifth order approximation. Here, the one-dimensional polynomial and trigonometrical basic splines of the fifth order approximation are constructed when the values of the function are known in each point of interpolation. For the construction of the spline, we use the discrete analogues of the first derivative and quadrature with the appropriate order of approximation. We compare the properties of these splines with splines which are constructed when the values of the first derivative of the function are known in each point of interpolation and the values of integral over each grid interval are given. The one-dimensional case can be extended to multiple dimensions through the use of tensor product spline constructs. Numerical examples are represented.

Язык оригиналаанглийский
Страницы (с-по)1011-1024
Число страниц14
ЖурналComputational Mathematics and Mathematical Physics
Том58
Номер выпуска7
DOI
СостояниеОпубликовано - 1 июл 2018

Отпечаток

Differential Polynomial
Quadrature Formula
Splines
Spline
Polynomials
Approximation Order
Interval
Approximation
Derivative
Derivatives
Tensor Product Splines
Interpolate
Interpolation
Grid
Polynomial Splines
Polynomial
Order of Approximation
Quadrature
System of equations
Tensors

Предметные области Scopus

  • Вычислительная математика

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Integro-Differential Polynomial and Trigonometrical Splines and Quadrature Formulas. / Бурова, Ирина Герасимовна; Евдокимова, Татьяна Олеговна; Родникова, Ольга Вадимовна.

В: Computational Mathematics and Mathematical Physics, Том 58, № 7, 01.07.2018, стр. 1011-1024.

Результат исследований: Научные публикации в периодических изданияхстатья

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T1 - Integro-Differential Polynomial and Trigonometrical Splines and Quadrature Formulas

AU - Бурова, Ирина Герасимовна

AU - Евдокимова, Татьяна Олеговна

AU - Родникова, Ольга Вадимовна

PY - 2018/7/1

Y1 - 2018/7/1

N2 - Abstract: This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following: the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed as the sum of products of the basic splines and the values of function in nodes and/or the values of its derivatives and/or the values of integrals of this function over subintervals. Basic splines are determined by using a solving system of equations which are provided by the set of functions. It is known that when integrals of the function over the intervals is equal to the integrals of the approximation of the function over the intervals then the approximation has some physical parallel. The splines which are constructed here satisfy the property of the fifth order approximation. Here, the one-dimensional polynomial and trigonometrical basic splines of the fifth order approximation are constructed when the values of the function are known in each point of interpolation. For the construction of the spline, we use the discrete analogues of the first derivative and quadrature with the appropriate order of approximation. We compare the properties of these splines with splines which are constructed when the values of the first derivative of the function are known in each point of interpolation and the values of integral over each grid interval are given. The one-dimensional case can be extended to multiple dimensions through the use of tensor product spline constructs. Numerical examples are represented.

AB - Abstract: This work is one of many that are devoted to the further investigation of local interpolating polynomial splines of the fifth order approximation. Here, new polynomial and trigonometrical basic splines are presented. The main features of these splines are the following: the approximation is constructed separately for each grid interval (or elementary rectangular), the approximation constructed as the sum of products of the basic splines and the values of function in nodes and/or the values of its derivatives and/or the values of integrals of this function over subintervals. Basic splines are determined by using a solving system of equations which are provided by the set of functions. It is known that when integrals of the function over the intervals is equal to the integrals of the approximation of the function over the intervals then the approximation has some physical parallel. The splines which are constructed here satisfy the property of the fifth order approximation. Here, the one-dimensional polynomial and trigonometrical basic splines of the fifth order approximation are constructed when the values of the function are known in each point of interpolation. For the construction of the spline, we use the discrete analogues of the first derivative and quadrature with the appropriate order of approximation. We compare the properties of these splines with splines which are constructed when the values of the first derivative of the function are known in each point of interpolation and the values of integral over each grid interval are given. The one-dimensional case can be extended to multiple dimensions through the use of tensor product spline constructs. Numerical examples are represented.

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KW - interpolation

KW - polynomial splines

KW - trigonometrical splines

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