In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational int...In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.展开更多
In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fra...In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.展开更多
Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing ...Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing the Thiele continued fraction interpolation, but also simplifies the interpolating polynomial coefficients with constant coefficients in the Thiele-Werner rational interpolation. Unattainable points and determinantal expression for this interpolation are considered. As an extension, some bivariate analogy is also discussed and numerical examples are given to show the validness of this method.展开更多
Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In ...Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In this paper,several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang.Numerical examples are given to show the effectiveness of the results in this paper.展开更多
基金The NNSF (10471055) of China and the National Grand Fundamental Research 973 Program (2004CB318000) of China.
文摘In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.
文摘In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.
基金Supported by the National Natural Science Foundation of China (Grant No.60473114)the Natural Science Foundation of Anhui Province (Grant No.070416227)
文摘Through adjusting the order of interpolation nodes, we gave a kind of modified Thiele-Werner rational interpolation. This interpolation method not only avoids the infinite value of inverse differences in constructing the Thiele continued fraction interpolation, but also simplifies the interpolating polynomial coefficients with constant coefficients in the Thiele-Werner rational interpolation. Unattainable points and determinantal expression for this interpolation are considered. As an extension, some bivariate analogy is also discussed and numerical examples are given to show the validness of this method.
基金the National Natural Science Foundation of China (No.60473114)the Anhui Provincial Natural Science Foundation (No.070416227)the Key Project Foundation of the Department of Education of Anhui Province (No.KJ2008A027)
文摘Newton interpolation and Thiele-type continued fractions interpolation may be the favoured linear interpolation and nonlinear interpolation,but these two interpolations could not solve all the interpolant problems.In this paper,several general frames are established by introducing multiple parameters and they are extensions and improvements of those for the general frames studied by Tan and Fang.Numerical examples are given to show the effectiveness of the results in this paper.
