A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points xo, x1, xn depends on th orderings of ...A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points xo, x1, xn depends on th orderings of these points and it is locally independent of the permutation of first n - 1 points. Moreover we define reciprocal difference from another point of view, get the relation between inverse difference and reciprocal difference and obtain the property that the reciprocal difference is globally independent of the permutation of the points.展开更多
By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and give...By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and given numerical example shows that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out computations for each step to obtain each convergent as done in [3].展开更多
文摘A compact determinantal representation for inverse difference is given. From the representation it is easy to know that the inverse difference of a function at some n + 1 points xo, x1, xn depends on th orderings of these points and it is locally independent of the permutation of first n - 1 points. Moreover we define reciprocal difference from another point of view, get the relation between inverse difference and reciprocal difference and obtain the property that the reciprocal difference is globally independent of the permutation of the points.
基金Supported by the Foundation for Excellent Young Teachers of the Ministry of Education of China and inpart by the Foundation f
文摘By means of the determinantal formulae for inverse and reciprocal differences with coincident data points, the limiting case of Thiele's interpolating continued fraction expansion is studied in this paper and given numerical example shows that the limiting Thiele's continued fraction expansion can be determined once for all instead of carrying out computations for each step to obtain each convergent as done in [3].
