Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.
A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a Gaussian quadrature formula of an extended Chebyshev system...A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a Gaussian quadrature formula of an extended Chebyshev system, and for a Gaussian Birkhoff quadrature formula are easily deduced.展开更多
文摘Discusses an extremal problem with Birkhoff interpolation constraints. Quadrature formula derived from an extremal problem; Overview of auxiliary lemmas; Derivation of some properties of polynomials.
基金Supported by the National Natural Science Foundation of China(No.11171100,10871065 and 11071064)by the Research Project of Fujian Agriculture and Forestry University(No.KXML2028A)
文摘A uniqueness theorem of a solution of a system of nonlinear equations is given. Using this result uniqueness theorems for power orthogonal polynomials, for a Gaussian quadrature formula of an extended Chebyshev system, and for a Gaussian Birkhoff quadrature formula are easily deduced.
