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THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER

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Journal of Computational mathematics 2001年第5期19卷 467-474页

作者： Dan-fu Han (department of mathematics, zhejiang university, hangzhou 310028, china) 浙江大学浙江杭州 310028

Establishes a convergent theorem for a family of iterations with cubic order by using general convergence hypotheses. Disadvantage of using the cubic majorizing function; Convergence of the majorizing sequence; Overvi... 详细信息

关键词： convergence majorizing method gamma-condition error estimate

THE CONVERGENCE OF DURAND-KERNER METHOD FOR SIMULTANEOUSLY FINDING ALL ZEROS OF THE POLYNOMIAL

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Journal of Computational mathematics 2000年第6期18卷 567-570页

作者： Dan-fu Han (department of mathematics, zhejiang university, hangzhou 310028, china) 浙江大学浙江杭州 310028

In this paper we propose the two kinds of different criterions and use them to judge the convergence of Durand-Kerner method and to compare the obtained results with other methods. [ABSTRACT FROM AUTHOR]

关键词： Durand-Kerner method convergence two kinds of criterions

APPLICATION OF NEWTON'S AND CHEBYSHEV'S METHODS TO PARALLEL FACTORJZATION OF POLYNOMIALS

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Journal of Computational mathematics 2001年第4期19卷 347-356页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus, zhejiang university, hangzhou 310028, china) 浙江大学浙江杭州 310028

In this paper it is shown m two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.

关键词： Newton's method Chebyshev's method Parallel iteration Factorization of polynomial.

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, hangzhou 310028, 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.

A FAMILY OF HIGH-ODER PARALLEL ROOTFINDERS FOR POLYNOMIALS

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Journal of Computational mathematics 2000年第3期18卷 283-288页

作者： Shi-ming Zheng (department of mathematics, Xixi Campus,zhejiang university, hangzhou, 310028, china) 浙江大学浙江杭州 310028

Presents a family of parallel iterations for finding all zeros of a polynomial without evaluation of derivatives. Construction of iterations; Convergence of the iterations; Details on the numerical examples.

关键词： parallel iteration zeros of polynomial order of convergence

Simple proofs of the Bedrosian equality for the Hilbert transform

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Science china mathematics 2009年第3期52卷 507-510页

作者： wang silei department of mathematics, zhejiang university, hangzhou 310027, china department of mathematics Zhejiang University Hangzhou 310027 China

Two simple proofs of Bedrosian theorem are given.

关键词： Hilbert transform Bedrosian theorem filter 42B20 42B25

Strong near-epoch dependence

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Science china mathematics 2004年第4期47卷 497-507页

作者： LIN Zhengyandepartment of mathematics, zhejiang university, hangzhou 310028, china 1. department of mathematics Zhejiang University 310028 Hangzhou China

We introduce a new class of dependent sequences of random variables, which is a subclass of near-epoch dependent sequences, but can also be approximated by mixing sequences. For this kind of sequences of random variables, we call them strong nearepoch dependent sequences, a p-order, p ＞ 2, (maximum) moment inequality is established under weaker dependence sizes.

关键词： near-epoch dependence, mixingale, strong near-epoch dependence, moment inequality, convergence.

Functional limit theorem for moving average processes generated by dependent random variables

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Progress in Natural Science:Materials International 2006年第3期16卷 266-273页

作者： LIN Zhengyan and LI Degui (department of mathematics, zhejiang university, hangzhou 310028, china) [a]department of mathematics Zhejiang University Hangzhou China

Let {Xt,t≥1} be a moving average process defined by , where {bj,j≥0} is a sequence of real num- bers and {ξt,-∞ 详细信息

Let {Xt,t≥1} be a moving average process defined by , where {bj,j≥0} is a sequence of real num- bers and {ξt,-∞

关键词： functional limit theorem long memory process linear process moving average process φ-mixing.

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.