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ON MATRIX UNITARILY INVARIANT NORM CONDITION NUMBER

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Journal of Computational mathematics 1998年第2期16卷 121-128页

作者： Dao-sheng Zheng (department of mathematics, East {2. Normal university, Shanghai 2.0062. {2.) E china Normal Univ Dept Math Shanghai 200062 Peoples R China

In this paper, the unitarily invariant norm \\.\\ on C-mxn is used. We first discuss the problem under what case, a rectangular matrix A has minimum condition number K(A) = \\A\\ \\A(+)\\, where A(+) designates the Moore-Penrose inverse of A; and under what condition, a square matrix A has minimum condition number for its eigenproblem? Then we consider the second problem, i.e., optimum of K(A) = \\A\\ \\A(-1)\\(2. in error estimation.

关键词： matrix unitarily invariant norm condition number

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 {2., Hangzhou 31002., 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

Jackson’s theorem in Q_p spaces

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Science china mathematics 2010年第2期53卷 367-372页

作者： CHEN YingWei 1 & REN GuangBin 1, 2. 1 department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china 2.department of mathematics, {2. of Aveiro, P-3810-193 Aveiro, Portugal 1. department of mathematics University of Science and Technology of China Hefei 230026 China2. Department of Mathematics University of Aveiro P-3810-193 Aveiro Portugal

A Jackson type inequality in Q p spaces is established, i.e., for any f (z) = Σ∞ j=0 ajzj ∈ Qp , 0≤p 1, and k-1 ∈ N,where ω(1/k, f, Q p ) is the modulus of continuity in Q p spaces and C(a) is an absolute const... 详细信息

关键词： Q p space BMOA polynomial approximation

Planar cubic hybrid hyperbolic polynomial curve and its shape classification

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Progress in Natural Science:Materials International 2004年第1期14卷 42-47页

作者： WANG Guozhao 1,2. * and YANG Qinmin 1,2. (1. Institute of Computer Graphics and Image Processing, 2. department of mathematics, Zhejiang university, Hangzhou 31002., {2.) Zhejiang Univ Inst Comp Graph & Image Proc Hangzhou 310027 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The planar cubic hybrid hyperbolic polynomial curves and cubic H Bézier curves are presented. The conditions leading to inflection points and singularities (cusps and loops) are investigated and the shape of these curves is classified. The conclusions enable us to detect inflection points and singularities and get an idea of how to preserve the fair shape when designing such curves.

关键词： hybrid hyperbolic polynomial curve H-Bézier curve shape classification inflection points singularities

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational mathematics 2000年第1期18卷 1-12页

作者： Bing-sheng He(department of mathematics, Nanjing {2., Naming 2.0093, china) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

A note on certain square functions on product spaces

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Science china mathematics 2006年第1期49卷 98-108页

作者： WANG Meng, CHEN Jiecheng2.& FAN Dashan department of mathematics, Zhejiang {2. (at Yuquan campus), Hangzhou 31002., china department of mathematics, Zhejiang {2. (at Xixi campus), Hangzhou 31002., china department of mathematics, {2. of Wisconsin-Milwaukee, Milwaukee, WI532.1, USA department of mathematics Zhejiang University [at Yuquan campus] Hangzhou 310027 China department of mathematics Zhejiang University [at Xixi campus] Hangzhou 310028 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI53201 USA

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

关键词： square function, Marcinkiewicz integral, product space.

THE GROWTH THEOREM FOR STARLIKE MAPPINGS ON BOUNDED STARLIKE CIRCULAR DOMAINS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 401-408页

作者： LIU TAISHUN (department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china)REN GUANGBIN (department of mathematics, {2. of Science and Technology of china, Hefei 2.002., china) Univ Sci & Technol china Dept Math Anhua 230026 Peoples R China

The authors obtain the growth and covering theorem for the class of normalized biholomorphic starlike mappings on bounded starlike circular *** type of domain discussed is rather general, since the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it. In the unit disc, it is just the famous growth and covering theorem for univalent *** theorem successfully realizes the initial idea of H. Cartan about how to extend geometric function theory from one variable to several complex variables.

关键词： Starlike mappings Growth theorem Starlike circular domains

The maximal super-singular integral operators on product spaces

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Science china mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2.3, 1department of mathematics, Xidian {2., Xi’an 710071, china 2.0} of mathematics, Zhejiang Normal {2., Jinhua 32.004, china 3department of mathematics, Zhejiang {2., Hangzhou 31002., china 1. department of mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2.0｜∫｜u｜〉ε1,｜v｜〉ε2.b1（｜u｜）b2.｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2.∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

GENUINE-OPTIMAL CIRCULANT PRECONDITIONERS FOR WIENER-HOPF EQUATIONS

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Journal of Computational mathematics 2001年第6期19卷 629-638页

作者： Fu-rong Lin (department of mathematics, Shantou {2., Shantou 515063,china) 汕头大学广东汕头 515063

Discusses the genuine-optimal circulant preconditioner for finite-section Wiener-Hopf equations. Definition of the genuine-optimal circulant preconditioner; Use of the preconditioned conjugate gradient method; Numeric... 详细信息

关键词： Wiener-Hopf equations circulant preconditioner preconditioned conjugate gradient method quadrature rules Hilbert-Schmidt norm