本文研究了基于Jacobi多项式J_n^((α,β))(x)(0<α,β<1)的零点{x_k}_1~n的Grnwald插值多项式G_n(f;x)=sum from k=1 to n (f(x_k)l_k^2(x)),证明了G_n(f;x)在(-1,1)内的任一闭子区间上一致收敛于连续函数f(x);从而拓广了Grnwal...本文研究了基于Jacobi多项式J_n^((α,β))(x)(0<α,β<1)的零点{x_k}_1~n的Grnwald插值多项式G_n(f;x)=sum from k=1 to n (f(x_k)l_k^2(x)),证明了G_n(f;x)在(-1,1)内的任一闭子区间上一致收敛于连续函数f(x);从而拓广了Grnwald所得结果。展开更多
In this paper the trigonometric interpolation polynomial operators Fn(g; r, t)are constructed. Fn(g; r, t) converge the function g(t) on (-∞, ∞) uniformly if thefunction g(t) ∈ C2π. The convergence order is the be...In this paper the trigonometric interpolation polynomial operators Fn(g; r, t)are constructed. Fn(g; r, t) converge the function g(t) on (-∞, ∞) uniformly if thefunction g(t) ∈ C2π. The convergence order is the best if g(t) ∈.j≤r (r≥1is nature number ).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
文摘本文研究了基于Jacobi多项式J_n^((α,β))(x)(0<α,β<1)的零点{x_k}_1~n的Grnwald插值多项式G_n(f;x)=sum from k=1 to n (f(x_k)l_k^2(x)),证明了G_n(f;x)在(-1,1)内的任一闭子区间上一致收敛于连续函数f(x);从而拓广了Grnwald所得结果。
文摘In this paper the trigonometric interpolation polynomial operators Fn(g; r, t)are constructed. Fn(g; r, t) converge the function g(t) on (-∞, ∞) uniformly if thefunction g(t) ∈ C2π. The convergence order is the best if g(t) ∈.j≤r (r≥1is nature number ).
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.
