For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by...For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.展开更多
This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide th...This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.展开更多
In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fracti...In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained.展开更多
A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical ...A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical example is given.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
Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of ...Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.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
As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared to...As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.展开更多
Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms ...Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,展开更多
基金The NNSF(10171026 and 60473114)of Chinathe Research Funds(2005TD03) for Young Innovation Group,Education Department of Anhui Province.
文摘For a univariate function given by its Taylor series expansion, a continued fraction expansion can be obtained with the Viscovatov＇s algorithm, as the limiting value of a Thiele interpolating continued fraction or by means of the determinantal formulas for inverse and reciprocal differences with coincident data points. In this paper, both Viscovatov-like algorithms and Taylor-like expansions are incorporated to yield bivariate blending continued expansions which are computed as the limiting value of bivariate blending rational interpolants, which are constructed based on symmetric blending differences. Numerical examples are given to show the effectiveness of our methods.
基金Project supported by the National Natural Science Foundation of China (No. 10171026, No. 60473114) the AnhuiProvincial Natural Science Foundation, China (No. 03046102)the Research Funds for Young InnovationGroup, Education Department of Anhui Province (No. 2005TD03).
文摘This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method.
文摘In this paper, a practical Werner-type continued fraction method for solving matrix valued rational interpolation problem is provided by using a generalized inverse of matrices. In order to reduce the continued fraction form to rational function form of the interpolants, an efficient forward recurrence algorithm is obtained.
基金Supported by the National Natural Science Foundation of China under Grant No. 10171026.
文摘A kind of triple branched continued fractions is defined by making use of Samel- son inverse and Thiele-type partial inverted di?erences [1]. In this paper, a levels-recursive algorithm is constructed and a numerical example is given.
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 Project Foundation of the Department of Education of Anhui Province(KJ2008A027,KJ2010B182,KJ2011B152,KJ2011B137)Supported by the Grant of Scientific Research Foundation for Talents of Hefei University(11RC05)Supported by the Grant of Scientific Research Foundation Hefei University(11KY06ZR)
文摘Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.
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.
基金Supported by the National Natural Science Foundation of China under Grant No.10171026 and in part by the Foundation for Excellent Young Teachers of the Ministry of Education of China and the Financially-Aiding Program for the Backbone Teachers of the Min
文摘As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.
基金Supported by-the National Natural Science Foundation of China
文摘Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,
基金supported by the Anhui Provincial Natural Science Foundation(No.070416227)the Natural Science Foundation of Anhui Provincial Education Depart ment under Grant(No.KJ2008A027)
