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FOURIER-CHEBYSHEV COEFFICIENTS AND GAUSS-TURAN QUADRATURE WITH CHEBYSHEV WEIGHT

Journal of Computational mathematics 2003年第2期21卷 189-194页

作者： shijun yang {2. wang (department of mathematics, zhejiang university, hangzhou 31002., China) department of mathematics Zhejiang University Hangzhou 310028

The main purpose of this paper is to derive an explicit expression for Fourier-Chebyshevcoefficientwhich is initiated by *** and***.

关键词： Fourier-Chebyshev coefficient Gauss-Turan quadrature

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The best quadrature based on given Hermite information for the Sobolev class KW^r[a,b]

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Science China mathematics 2006年第8期49卷 1146-1152页

作者： wang xinghua & yang shijun department of mathematics, zhejiang university,{2., China department of mathematics, hangzhou Normal College, hangzhou 310036, China department of mathematics Zhejiang University Hangzhou 310028 China department of mathematics Hangzhou Normal College Hangzhou 310036 China

As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given Hermite *** work reports the results on the best quadrature based on the given Hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

关键词： Sobolev class, Hermite information, perfect spline, optimal recovery, best quadrature.

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On solving equations of algebraic sum of equal powers

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Science China mathematics 2006年第9期49卷 1153-1157页

It is well known that a system of equations of sum of equal powers can be converted to an algebraic equation of higher degree via Newton's identities. This is the Viete-Newton theorem. This work reports the generalizations of the Viete-Newton theorem to a system of equations of algebraic sum of equal powers. By exploiting some facts from algebra and combinatorics,it is shown that a system of equations of algebraic sum of equal powers can be converted in a closed form to two algebraic equations, whose degree sum equals the number of unknowns of the system of equations of algebraic sum of equal powers.

关键词： algebraic sum of equal powers, Newton's identities, system of equations,roots of a polynomial.

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