2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding in...2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.展开更多
Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the ＂jumps＂ are approximated by solution of a system of linear equations. The accu...Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the ＂jumps＂ are approximated by solution of a system of linear equations. The accuracy of the ＂jump＂ approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates.展开更多
The saturation rate and class of (0,m1,m2, …,mq) trigonometric inter polation operators in . spaces have been determined by Cavaretta and Selvaraj. In this paper, we consider the convergence and saturation problems o...The saturation rate and class of (0,m1,m2, …,mq) trigonometric inter polation operators in . spaces have been determined by Cavaretta and Selvaraj. In this paper, we consider the convergence and saturation problems of these operators in (1≤p≤∞) and obtain complete results.展开更多
Proposed in the paper is a trigonometric interpolation method for efficient determination of turbomachinery blade aero-damping curves which are required in a flutter assessment.The trigonometric interpolation method w...Proposed in the paper is a trigonometric interpolation method for efficient determination of turbomachinery blade aero-damping curves which are required in a flutter assessment.The trigonometric interpolation method was proposed to be incorporated with the widely used travelling wave method to replace the influence coefficient method.Through analyzing aero-damping/worksum at a few carefully chosen nodal diameters,trigonometric interpolation was applied through existing data points to get aero-damping/worksum at the rest nodal diameters.The proposed approach is much more efficient than the travelling wave method for determining the aero-damping curve of a blade.In principle,the method can be as efficient as the influence coefficient method.Unlike the influence coefficient method,the trigonometric interpolation method does not involve linear superposition,and it can include nonlinear effect and is expected to be more accurate.Two test cases were provided to validate the proposed method and demonstrate its effectiveness.The method is not only effective,but also very easy to be incorporated into existing widely used aero-damping/worksum analysis system using the travelling wave method.展开更多
In this paper, we give a necessary and sufficient condition of sequence of nodes, such that, the error of trigonometric interpolation for analytic function converges to 0.
Due to the deficiency of sliding Lagrange polynomial interpolation, the author proposes a new interpolation method, which considers the physical character of satellite movement in coordinate transformation and reasona...Due to the deficiency of sliding Lagrange polynomial interpolation, the author proposes a new interpolation method, which considers the physical character of satellite movement in coordinate transformation and reasonable selection of interpolation function. Precision of the two methods is compared by a numerical example. The result shows that the new method is superior to the sliding Lagrange polynomial interpolation in interpolation and extrapolation, especially in extrapolation that is over short time spans.展开更多
In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of to...In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.展开更多
Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with inte...Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.展开更多
By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between...By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.展开更多
文摘2-periodic trigonometric interpolation problems on 2n equidistant nodes and 4n+1 equi- distant nodes are considered respectively.Regularity theorems,fundamental polynomials and convergence rate of the corresponding interpolations are given here.
基金Supported in part by grant PS 1867 from the Armenian National Science and Education Fund (ANSEF) based in New York, USA
文摘Convergence acceleration of the classical trigonometric interpolation by the Eckhoff method is considered, where the exact values of the ＂jumps＂ are approximated by solution of a system of linear equations. The accuracy of the ＂jump＂ approximation is explored and the corresponding asymptotic error of interpolation is derived. Numerical results validate theoretical estimates.
文摘The saturation rate and class of (0,m1,m2, …,mq) trigonometric inter polation operators in . spaces have been determined by Cavaretta and Selvaraj. In this paper, we consider the convergence and saturation problems of these operators in (1≤p≤∞) and obtain complete results.
基金supported by China’s 111 project(Grant No.B17037)National Natural Science Foundation of China(Grant No.51976172)National Science and Technology Major Project(2017-II-0009-0023)。
文摘Proposed in the paper is a trigonometric interpolation method for efficient determination of turbomachinery blade aero-damping curves which are required in a flutter assessment.The trigonometric interpolation method was proposed to be incorporated with the widely used travelling wave method to replace the influence coefficient method.Through analyzing aero-damping/worksum at a few carefully chosen nodal diameters,trigonometric interpolation was applied through existing data points to get aero-damping/worksum at the rest nodal diameters.The proposed approach is much more efficient than the travelling wave method for determining the aero-damping curve of a blade.In principle,the method can be as efficient as the influence coefficient method.Unlike the influence coefficient method,the trigonometric interpolation method does not involve linear superposition,and it can include nonlinear effect and is expected to be more accurate.Two test cases were provided to validate the proposed method and demonstrate its effectiveness.The method is not only effective,but also very easy to be incorporated into existing widely used aero-damping/worksum analysis system using the travelling wave method.
文摘In this paper, we give a necessary and sufficient condition of sequence of nodes, such that, the error of trigonometric interpolation for analytic function converges to 0.
基金supported by the PhD Excellence Fund of Information Engineering University(S201307)
文摘Due to the deficiency of sliding Lagrange polynomial interpolation, the author proposes a new interpolation method, which considers the physical character of satellite movement in coordinate transformation and reasonable selection of interpolation function. Precision of the two methods is compared by a numerical example. The result shows that the new method is superior to the sliding Lagrange polynomial interpolation in interpolation and extrapolation, especially in extrapolation that is over short time spans.
文摘In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.
文摘Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.
文摘By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.
