1.

COMPUTING TRACE OF FUNCTION OF MATRIX





郑洪斌《高等学校计算数学学报(英文版)》,2000年第2期


1 IntroductionIn some applications such as computational phySics, one often computes det~inant Ofmatrix and trace Of function of matrix. For ~ fun~ such as f(x) ~1/x or f(x) In (x) computing tr(f(A) ),i. e. tr(A' ) or In(det(A) ) respeCtively, may be highly sensitiveproblems. When the matrix she n is small, we can compute these problemS explicits by usaldense ~x computation methods L6J. General speaking, such methods require O(n3) floating point OPerations. However, when n atomes larg…

2.

Affineperiodic solutions by averaging methods





Jiamin Xing Xue Yang Yong Li《中国科学 数学(英文版)》,2018年第61卷第3期


This paper concerns the existence of affineperiodic solutions for perturbed affineperiodic systems.This kind of affineperiodic solutions has the form of x(t+T)≡Qx(t) with some nonsingular matrix Q,which may be quasiperiodic when Q is an orthogonal matrix. It can be even unbounded but x(t)/x(t) is quasiperiodic,like a helical line. for example x(t)=e~(at)(cos ωt, sin ωt), when Q is not an orthogonal matrix. The averaging method of higher order for finding affineperiodic solutions is given by topological degree.

3.

BLOCK BIDIAGONALIZATION METHODS FOR MULTIPLE NONSYMMETRIC LINEAR SYSTEMS





戴华《高等学校计算数学学报(英文版)》,2001年第10卷第2期


1 IntroductionMany applications require the solution of large nonsymmetric linear equations withmultiple righthand sidesAX =B ( 1 )where A is a real nonsymmetric matrix ofordern,and X=[x(1 ) ,… ,x(s) ] and B=[b(1 ) ,… ,b(s) ] are rectangular matrices of dimension n×s with s n.Most of iterative methods forthe solution of nonsymmetric linear systems with a single righthand side may be used tosolve( 1 ) by solving the s linear systems individually.But iterative methods,such asKrylov subs…

4.

INADMISSIBILITY AND ADMISSIBILITY RESULTS FOR UNBIASED LOSS ESTIMATORS BASED ON GAUSSMARKOV ESTIMATORS





吴启光《应用数学学报(英文版)》,1993年第3期


Let Y be distributed according to an nvariate normal distribution with a mean Xβ and a nonsingular covariance matrix σ~2V,where both X and V are known,β∈R~p is a parameter,σ>0 is known or unknown.Denote β=(X'V~1X)X'V~1Y and S~2=(YXβ)'V~(1)(YXβ).Assume that Eβ is linearly estimable.When σ is known,it is proved that the unbiased loss estimator σ~2tr(F(X'V~1X)F')of(FβFβ)'(FβFβ)is admissible for rank (F)=k≤4 and inadmissible for k≥5 with the squared error loss[a(FβFβ)'(FβFβ)]~2 When σ is unknown and rank (X)

5.

A GENERALIZATION OF A PROPOSITION ON EXPONENTIAL DICHOTOMY 被引次数：2





史金麟《Annals of Differential Equations》,2000年第1期


1 Introduction and Statement of TheoremConsider systemx' = A(t)x f(t, x), (l.1)where x E R", A(t) is a continuous matrix function, f: R x R"  R" is acontinuous function.We say that the linear differential equation X' = A(t)x admits an exponential dichotomy, if it has a fundamental matrix X(t) such thatIX(t)PX'(s)l 5 K' ea(ts) for s S t,(1.2)IX(t)(I  P)X'(s)I 5 K' ea(st) for s 2 t, (1'2)where P is a projection (P' = P), K and a are positive constants.Remark Without …

6.

AN ADAPTIVE VARIANT OF CGNR ALGORITHM





李春光《高等学校计算数学学报(英文版)》,2001年第10卷第1期


1 IntroductionConsider large linear systemAx =b, ( 1 .1 )where A and b are given,A isa nonsingularn×n real matrix,and b is an nvector.When A issymmetric positive definite ( s.p.d.) ,the classical conjugate gradient method ( CG) [7] used inconjunction with incomplete factorization preconditioning technique[1 0 ] is a succesful method inview of the high robustness and efficiency.But for general nons.p.d.systems,the situationis less satisfactory.The generalized minimal residual algorithm( …

7.

MuellerMatrixBased Differential Rotation Method for Precise Measurement of Fiber Birefringence Vector





李政勇 吴重庆 尚超 余向志《中国物理快报》,2010年第27卷第10期


The method of complete polar decomposition for arbitrary Mueller matrixes is introduced to analyze the birefringence vector induced in a fiber, and then based on the Mueller matrix （MM） method, three kinds of computation methods including the absolute, the relative, and the differential rotation methods are proposed and investigated in detail. A computercontrolled measure system is employed to measure the Mueller matrix and birefringence vector for a 2.5km fiber system with length 5 mm under lateral press in complicated environment with much perturbation. Experimental results show that the differential rotation （DR） method is the optimal approach to achieve fiber birefringence vectors in a large dynamic range of lateral press on fibers in perturbed situations, which reaches the highest linearity of 0.9998 and average deviation below 2.5%. Further analyses demonstrate that the DR method is also available for accurate orientation of lateral press direction and the average deviation is about 1.1°.

8.

ANALYSIS OF A MECHANICAL SOLVER FOR LINEAR SYSTEMS OF EQUATIONS





Luis Vazquez 《计算数学(英文版)》,2001年第1期


1. Introduction/ A new approaCh to solve systems of linear eqttations, equlvaleat to solve the ~ion of adamped harmonic oscillator, has been PrOPosed in a previous paper[11. Due to this parallelism,we call such methods Mechanical Solvers for systems of linear equations. The present study isdevoted to the analysis of these methods.Let be the linear systemwhere we assume that A is an m x m nonsingular matriX (i.e. the system has a ~ solution).We may associate to it the Newton's equation for …

9.

SOME PROPERTIES OF ROSEN’S MLE FOR GENERAL DISTRIBUTIONS





崔恒建 陈秋华《数学物理学报(B辑英文版)》,2001年第3期


1 IntroductionConsider the lnultivariate linear model (MLM) as follows:mX = Z AiBiC E (1)i= 1where X, Ai, Bi and C are p x nfp x qi(qi 5 p), qi x ki and ki x n matrices respectively, Z is ap x p definite positive matrix with p(C1) p 5 n and R(CL) G R(Cfu,) g' g R(CI), p(.)and R(.) stand for the rank and the colunu spanned linear space Of a matriX respbctively.e = (e1,'2,... f e.), e1le21',f n are iid. pvariate random vectors with D(e1) = Z > 0,E(El) = 0, A: aild C: are …

10.

ON AUGMENTED LAGRANGIAN METHODS FOR SADDLEPOINT LINEAR SYSTEMS WITH SINGULAR OR SEMIDEFINITE （1, 1） BLOCKS





Tatiana S. Martynova《计算数学(英文版)》,2014年第3期


An effective algorithm for solving large saddlepoint linear systems, presented by Krukier et al., is applied to the constrained optimization problems. This method is a modification of skewHermitian triangular splitting iteration methods. We consider the saddlepoint linear systems with singular or semidefinite （1, 1） blocks. Moreover, this method is applied to precondition the GMRES. Numerical results have confirmed the effectiveness of the method and showed that the new method can produce highquality preconditioners for the Krylov subspace methods for solving large sparse saddlepoint linear systems.

11.

The existence of nontrivial solutions to a semilinear elliptic system on without the ambrosettirabinowitz condition





李工宝 王春花《数学物理学报(B辑英文版)》,2010年第30卷第6期


In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {△u＋u=f（x,v）,x∈RN,△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentrationcompactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the AmbrosettiRabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 36283638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925954, 2004] concerning （0.1） when f and g are asymptotically linear.

12.

NONDESCENT SUBGRADIENT METHOD FOR NONSMOOTH CONSTRAINED MINIMIZATION





徐慧福《高等学校计算数学学报(英文版)》,1994年第2期


A kind of nondecreasing subgradient algorithm with appropriate stopping rule has been proposed for nonsmooth constrained minimization problem. The dual theory is invoked in dealing with the stopping rule and general global minimiizing algorithm is employed as a subroutine of the algorithm. The method is expected to tackle a large class of nonsmooth constrained minimization problem.

13.

THE ASYMPTOTIC PROPERTIES OF THE MULTICHANNEL AUTOREGRESSIVE SPECTRAL ESTIMATES





陈兆国《应用数学学报(英文版)》,1988年第1期


If we fit a rvector stationary time series using observations x(1),…,x(T) with AR models x(t)+a_k~(T)(1)x(t1)+…+a_k~(T)(k)x(tk)=ε(t),then the spectral density f(λ) of {x(t)} can be estimated by f_k~(T)(λ)=(2π)~(1)A_k~(T)(e~(6λ))~(1)Σ_k~(T) A_k~(T)(e~(tλ))~(k),are estimates of the variance matrix Σ of ε(t),the residuals of the best linear prediction.By extending some results for the scalar case,this paper treats the asymptotic properties of the estimates in the multichannel case.

14.

A FAST NUMERICAL METHOD FOR INTEGRAL EQUATIONS OF THE FIRST KIND WITH LOGARITHMIC KERNEL USING MESH GRADING





QiyuanChen TaoTang ZhenhuanTeng《计算数学(英文版)》,2004年第22卷第2期


The aim of this paper is to develop a fast numerical method for twodimensional boundary integral equations of the first kind with logarithm kernels when the boundary of the domain is smooth and closed. In this case, the use of the conventional boundary element methods gives linear systems with dense matrix. In this paper, we demonstrate that the dense matrix can be replaced by a sparse one if appropriate graded meshes are used in the quadrature rules. It will be demonstrated that this technique can increase the numerical efficiency significantly.

15.

GENERALIZED MATRIX MULTISPLITTING RELAXATION METHODS AND THEIR CONVERGENCE 被引次数：4





白中治 王德人《高等学校计算数学学报(英文版)》,1993年第1期


In this paper, we set up a general framework of parallel matrix mullisplitting relaxation methods for solving large scale system of linear equations. We investigate the convergence properties of this framework and give several sufficient conditions ensuring it to converge as well as diverge. At last, we conclude a necessary and sufficient condition for the convergence of this framework when the coefficient matrix is an Lmatrix.

16.

BLOCKSYMMETRIC AND BLOCKLOWERTRIANGULAR PRECONDITIONERS FOR PDECONSTRAINED OPTIMIZATION PROBLEMS＊





Guofeng Zhang Zhong Zheng《计算数学(英文版)》,2013年第4期


Optimization problems with partial differential equations as constraints arise widely in many areas of science and engineering, in particular in problems of the design. The solution of such class of PDEconstrained optimization problems is usually a major computational task. Because of the complexion for directly seeking the solution of PDEconstrained op timization problem, we transform it into a system of linear equations of the saddlepoint form by using the Galerkin finiteelement discretization. For the discretized linear system, in this paper we construct a blocksymmetric and a blocklowertriangular preconditioner, for solving the PDEconstrained optimization problem. Both preconditioners exploit the structure of the coefficient matrix. The explicit expressions for the eigenvalues and eigen vectors of the corresponding preconditioned matrices are derived. Numerical implementa tions show that these block preconditioners can lead to satisfactory experimental results for the preconditioned GMRES methods when the regularization parameter is suitably small.

17.

Electronic structures and energy band properties of Be and Sdoped wurtzite ZnO





郑树文 范广涵 何苗 张涛《中国物理 B》,2014年第6期


The energy band properties, density of states, and band alignment of the BexZn1xO1ySy alloy （Be and Sdoped wurtzite ZnO） are investigated by the firstprinciples method. BexZn1xO1ySy alloy is a direct band gap semiconductor, the valence band maximum （VBM） and the conduction band minimum （CBM） of BexZn1xO1ySy are dominated by S 3p and Zn 4s states, respectively. The band gap and lattice constant of BexZn1xO1ySy alloy can be modulated by changing the doped content values x and y. With the increase in Be content value x in the BexZnlxOlySy alloy, the band gap increases and the lattice constant reduces, but the situation is just the opposite when increasing the S content value y in the BexZn1xO1ySy alloy. Because the lattice constant of Be0.375Zn0.625O0.75S0.25 alloy is well matched with that of ZnO and its energy gap is large compared with that of ZnO, so the Be0.375Zn0.625O0.75S0.25 alloy is suitable for serving as the blocking material for a highquality ZnObased device.

18.

Regularity for quasilinear degenerate elliptic equations with VMO coefficients





Shen Zhou Zheng《数学学报(英文版)》,2008年第24卷第11期


In this paper we establish an interior regularity of weak solution for quasilinear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1  n/q, 1  n/γ}.

19.

Weighted Regression and the General Influence Measure





杨虎《应用数学》,1991年第1期


Consider the weighted linear regression model: WY=WXβ ε, E(ε)=0, Cov(ε) =σ~2I, (1) where Y and ε are nvectors, X is a n×p design matrix, β is a pvector, w=diag(ω_1,ω_2,…,ω_n)σ. When W=I, (1) changes into a general GaussMarkov linear model. The least square estimate (LSE) of β in (1) is β_(W~2)= (X'W~2X)~(1)X'W~2Y, it's the generalized least square estimates (GLSE) of β in the heteroscedastic linear model: Y=Xβ ε, E(ε)=0 , cov(ε)=σ~2W~(2), (2) when W= I, β_1= (X'X)~(1)X~1Y is LSE of the parameter β in the GaussMarkov model. We want to know the disturbation △Y_W of Y_W=WXβ_W, when the disturbation △W~2 exists. When W=I, △W~2=Ω=diag (0,0, …, 1,0,…,0)(only the ith diagonal element is1),△Y_I represents the disturbation of the predicated

20.

An efficient timeintegration method for nonlinear dynamic analysis of solids and structures





LIU TianYun LI QingBin ZHAO ChongBin《中国科学:物理学 力学 天文学(英文版)》,2013年第4期


This paper presents an efficient timeintegration method for obtaining reliable solutions to the secondorder nonlinear dynamic problems in structural engineering. This method employs both the backwardacceleration differentiation formula and the trapezoidal rule, resulting in a selfstarting, single step, secondorder accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics: (1) it is applicable to linear as well as general nonlinear analyses; (2) it does not involve additional variables (e.g. Lagrange multipliers) and artificial parameters; (3) it is a singlesolver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and (4) it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses.
