ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR A CLASS OF THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATION

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＴＨＥＳＹＳＴＥＭＳＯＦＭＩＸＥＤＭＯＮＯＴＯＮＥＯＰＥＲＡＴＯＲＥＱＵＡＴＩＯＮＳＷＩＴＨＡＰＰＬＩＣＡＴＩＯＮＳＨＥＮＰＥＩＬＯＮＧ...     

THE REAL CUBE DIFFERENTIAL SYSTEM WITH THREE REAL STRAIGHT LINE SOLUTIONS AND TWO CONJUGATE COMPLEX STRAIGHT LINE SOLUTIONS

ＴＨＥ　ＲＥＡＬ　ＣＵＢＥ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＳＹＳＴＥＭ　ＷＩＴＨ　ＴＨＲＥＥ　ＲＥＡＬ　ＳＴＲＡＩＧＨＴ　ＬＩＮＥ　ＳＯＬＵＴＩＯＮＳ　ＡＮＤ　ＴＷＯ　ＣＯＮＪＵＧＡＴＥ　ＣＯＭＰＬＥＸ　ＳＴＲＡＩＧＨＴ　ＬＩＮＥ　ＳＯＬＵＴＩＯＮＳＴＨ...     

FIXED POINTS AND COUPLED FIXED POINTS FOR INCREASING OPERATORS WITH APPLICMIONS TO DIFFERENTIAL INCLUSIONS IN BANACH SPACES

ＦＩＸＥＤＰＯＩＮＴＳＡＮＤＣＯＵＰＬＥＤＦＩＸＥＤＰＯＩＮＴＳＦＯＲＩＮＣＲＥＡＳＩＮＧＯＰＥＲＡＴＯＲＳＷＩＴＨＡＰＰＬＩＣＭＩＯＮＳＴＯＤＩＦＦＥＲＥＮＴＩＡＬＩＮＣＬＵＳＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺＨＡＮＧＳＨＩＳＨＥＮＧＡＮＤＨＵ...     

ADMISSIBILITY OF LINEAR ESTIMATE OF REGRESSION COEFFICIENTS IN GROWTH CURVE MODEL UNDER MATRIX LOSS

ＡＤＭＩＳＳＩＢＩＬＩＴＹＯＦＬＩＮＥＡＲＥＳＴＩＭＡＴＥＯＦＲＥＧＲＥＳＳＩＯＮＣＯＥＦＦＩＣＩＥＮＴＳＩＮＧＲＯＷＴＨＣＵＲＶＥＭＯＤＥＬＵＮＤＥＲＭＡＴＲＩＸＬＯＳＳＷＡＮＧＸＵＥＲＥＮ（王学仁）（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓ，...     

EXISTENCE AND UNIQUENESS OF GLOBAL SOLUTION FOR CERTAIN NONLINEAR DEGENERATE PARABOLIC SYSTEMS

ＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＦＯＲＣＥＲＴＡＩＮＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＰＡＲＡＢＯＬＩＣ　ＳＹＳＴＥＭＳＬＵＧＵＯＦＵ（卢国富）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｐｕｔｉ...     

A NOTE ON REGULARITY AND EXISTENCE OF SOLUTIONS FOR A CLASS OF NON－UNIFORMLY DEGENERATE ELLIPTIC EQUATIONS

ＡＮＯＴＥＯＮＲＥＧＵＬＡＲＩＴＹＡＮＤＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮ－ＵＮＩＦＯＲＭＬＹＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＬＩＪＵＮＪＩＥ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＺｈｅｊｉａｎｇＵｎｉ...     

A COMPLETE METRIC OF POSITIVE CURVATURE ON R~n AND EXISTENCE OF CLOSED GEODESICS

ＡＣＯＭＰＬＥＴＥＭＥＴＲＩＣＯＦＰＯＳＩＴＩＶＥＣＵＲＶＡＴＵＲＥＯＮＲ~ｎＡＮＤＥＸＩＳＴＥＮＣＥＯＦＣＬＯＳＥＤＧＥＯＤＥＳＩＣＳ￥ＺＨＵＤＡＸＩＮ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙｌＴｉａｎｊ?..     

A NOTE FOR THE TOPOLOGICAL CLASSIFICATION OF STRUCTURALLY STABLE QUADRATIC DIFFERENTIAL SYSTEMS WITHOUT LIMIT CYCLES

ＡＮＯＴＥＦＯＲＴＨＥＴＯＰＯＬＯＧＩＣＡＬＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＳＴＲＵＣＴＵＲＡＬＬＹＳＴＡＢＬＥＱＵＡＤＲＡＴＩＣＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭＳＷＩＴＨＯＵＴＬＩＭＩＴＣＹＣＬＥＳ￥ＹｅＷｅｉｙｉｎ（叶惟寅）（ＮａｎｊｉｎｇＮ...     

THE SOLUTION OF _b－EQUATION OF （P，Q）－FORMS AND IT＇S L~P＆HOLDER ESTIMATES ON A STEIN MANIFOLD

ＴＨＥＳＯＬＵＴＩＯＮＯＦ_ｂ－ＥＱＵＡＴＩＯＮＯＦ（Ｐ，Ｑ）－ＦＯＲＭＳＡＮＤＩＴ＇ＳＬ￣Ｐ＆ＨＯＬＤＥＲＥＳＴＩＭＡＴＥＳＯＮＡＳＴＥＩＮＭＡＮＩＦＯＬＤ￥ＷｕＸｉａｏｑｉｎ（ＤｅｐｔｏｆＭａｔｈ，ＪｉｍｅｉＴｅａｃｈｅｒｓＣｏｌｌｅｇｅＸｉａ?..     

MIXED BOUNDARY VALUE PROBLEM FOR SECOND－ORDER SYSTEM OF DIFFERENTIAL EQUATIONS OF THE ELLIPTIC TYPE

（陈庆祥）ＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＦＯＲＳＥＣＯＮＤ－ＯＲＤＥＲＳＹＳＴＥＭＯＦＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＯＦＴＨＥＥＬＬＩＰＴＩＣＴＹＰＥ￥ＣｈｅｎＱｉｎｇｘｉａｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｚｈｏｎｇｓ...     

The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method

In this paper, a scheme is developed to study numerical solution of the space- and time-fractional Burgers equations with initial conditions by the variational iteration method (VIM). The exact and numerical solutions obtained by the variational iteration method are compared with that obtained by Adomian decomposition method (ADM). The results show that the variational iteration method is much easier, more convenient, and more stable and efficient than Adomian decomposition method. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.     

无罚函数和滤子的一个新的QP-free方法

通过构造一个等价于原约束问题一阶KKT条件的非光滑方程组, 提出一类新的QP-free方法. 在迭代中采用了无罚函数和无滤子线搜索方法, 在此基础上, 通过牛顿-拟牛顿迭代得到满足KKT最优条件的解, 并证明该算法是可实现、具有全局收敛性. 另外, 在较弱条件下可以证明该方法具有超线性收敛性.     

新的滤子方法

本文定义了一种新的滤子方法,并提出了求解光滑不等式约束最优化问题的滤子QP-free非可行域方法.通过乘子和分片线性非线性互补函数,构造一个等价于原约束问题一阶KKT条件的非光滑方程组.在此基础上,通过牛顿-拟牛顿迭代得到满足KKT最优条件的解,在迭代中采用了滤子线搜索方法,证明了该算法是可实现,并具有全局收敛性.另外,在较弱条件下可以证明该方法具有超线性收敛性.     

ON CONVERGENCE OF NOUREIN ITERATIONS FOR SIMULTANEOUS FINDING ALL ZEROS OF A POLYNOMIAL

1. IntroductionSuppose thatn nf(t) = bait"--' = fi(t -- (i), ac = 1 (1)i=0 j=1is a monic polynomial of degree n with complex coefficients. Some authors have studiedthe parallel iterations without derivatives for simultaneous finding all zeros fi, (2,'. 5 (nof f(t) (see [1]--[10],[13], [14], [16]). The famous one is Durand-Kerner iteration withthe formxt ' = xo ~ ac i = 1,2,' ',n? k ~ 0, 1,' t (2)where xo is the k--th approximation of fi(1 5 i 5 n) andf(xf)ac = M, i = 1,' 'In, k ~ 0,1,..…     

A new single-step iteration method for solving complex symmetric linear systems

For solving a class of complex symmetric linear systems, we introduce a new single-step iteration method, which can be taken as a fixed-point iteration adding the asymptotical error (FPAE). In order to accelerate the convergence, we further develop the parameterized variant of the FPAE (PFPAE) iteration method. Each iteration of the FPAE and the PFPAE methods requires the solution of only one linear system with a real symmetric positive definite coefficient matrix. Under suitable conditions, we derive the spectral radius of the FPAE and the PFPAE iteration matrices, and discuss the quasi-optimal parameters which minimize the above spectral radius. Numerical tests support the contention that the PFPAE iteration method has comparable advantage over some other commonly used iteration methods, particularly when the experimental optimal parameters are not used.     

A multigrid method for constrained optimal control problems

We consider the fast and efficient numerical solution of linear-quadratic optimal control problems with additional constraints on the control. Discretization of the first-order conditions leads to an indefinite linear system of saddle point type with additional complementarity conditions due to the control constraints. The complementarity conditions are treated by a primal-dual active set strategy that serves as outer iteration. At each iteration step, a KKT system has to be solved. Here, we develop a multigrid method for its fast solution. To this end, we use a smoother which is based on an inexact constraint preconditioner.We present numerical results which show that the proposed multigrid method possesses convergence rates of the same order as for the underlying (elliptic) PDE problem. Furthermore, when combined with a nested iteration, the solver is of optimal complexity and achieves the solution of the optimization problem at only a small multiple of the cost for the PDE solution.     

Analysis and modificaton of Newton's method for algebraic Riccati equations

When Newton's method is applied to find the maximal symmetric solution of an algebraic Riccati equation, convergence can be guaranteed under moderate conditions. In particular, the initial guess need not be close to the solution. The convergence is quadratic if the Fréchet derivative is invertible at the solution. In this paper we examine the behaviour of the Newton iteration when the derivative is not invertible at the solution. We find that a simple modification can improve the performance of the Newton iteration dramatically.

     

构造Banach空间上非线性方程解的预解式迭代过程

一 设X是实Banach空间,X是它的对偶空间。A:X→2~X为一集合值非线性映象,0∈A_x称为关于A的非线性映象方程。对于任一确定的正实数λ,设逆映象 J_λ=(I λA)~(-1)存在并单值,称J_λ为A的预解式算子,并称     

A single-step HSS method for non-Hermitian positive definite linear systems

In this paper, based on the Hermitian and skew-Hermitian splitting (HSS) iteration method, a single-step HSS (SHSS) iteration method is introduced to solve the non-Hermitian positive definite linear systems. Theoretical analysis shows that, under a loose restriction on the iteration parameter, the SHSS method is convergent to the unique solution of the linear system. Furthermore, we derive an upper bound for the spectral radius of the SHSS iteration matrix, and the quasi-optimal parameter is obtained to minimize the above upper bound. Numerical experiments are reported to the efficiency of the SHSS method; numerical comparisons show that the proposed SHSS method is superior to the HSS method under certain conditions.     

新的滤子方法(英)

本文定义了一种新的滤子方法,并提出了求解光滑不等式约束最优化问题的滤子QP-free非可行域方法. 通过乘子和分片线性非线性互补函数,构造一个等价于原约束问题一阶KKT条件的非光滑方程组.在此基础上, 通过牛顿-拟牛顿迭代得到满足KKT最优条件的解,在迭代中采用了滤子线搜索方法,证明了该算法是可实现,并具有全局收敛性. 另外,在较弱条件下可以证明该方法具有超线性收敛性.