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Full-Text Articles in Physical Sciences and Mathematics
On An Extension Of Abel-Gontscharoff's Expansion Formula, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue
On An Extension Of Abel-Gontscharoff's Expansion Formula, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue
Tian-Xiao He
We present a constructive generalization of Abel-Gontscharoff’s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for the constructing the basis functions of the interpolants are given.
On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He
On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He
Tian-Xiao He
By using Gould's annihilation coefficients, we obtain an explicit fundamental polynomials of Multivariate Abel-Gontscharoff Interpolation and its remainder expression.
On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue
On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue
Tian-Xiao He
In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.