基于Samelson逆的向量值连分式的收敛准则

The aim of this work is to give some criteria on the convergence of vector valued continued fractions defined by Samelson inverse. We give a new approach to prove the convergence theory of continued fractions. First, by means of the modified classical backward recurrence relation, we obtain a formula between the m-th and n-th convergence of vector valued continued fractions. Second, using this formula, we give necessary and sufficient conditions for the convergence of vector valued continued fractions.     

Trigonometric series with a generalized monotonicity condition

In this paper,we consider numerical and trigonometric series with a very general monotonicity condition.First,a fundamental decomposition is established from which the sufficient parts of many classical results in Fourier analysis can be derived in this general setting.In the second part of the paper a necessary and sufficient condition for the uniform convergence of sine series is proved generalizing a classical theorem of Chaundy and Jolliffe.     

ON THE CONVERGENCE OFSPLITTINGS FOR A Z-MATRIX

In this paper, first we present a characterization of semiconvergence for nonnegative splittings of a singular Z-mattix, which generalizes the corresponding result of . Second, a characterization of convergence for L1-regular splittings of a singular E-matrix is given, which im-prove the resuh of [3]. Third, convergence of weak nonnegative splittings and regular splittings isdiscussed, and we obtain some necessary and sufficient conditions such that the splittings of a Z-matrix converge,     

The Convergence of the Sums of Independent Random Variables Under the Sub-linear Expectations

Let {Xn;n≥1} be a sequence of independent random variables on a probability space(Ω,F,P) and Sn=∑k=1n Xk.It is well-known that the almost sure convergence,the convergence in probability and the convergence in distribution of Sn are equivalent.In this paper,we prove similar results for the independent random variables under the sub-linear expectations,and give a group of sufficient and necessary conditions for these convergence.For proving the results,the Levy and Kolmogorov maximal inequalities for independent random variables under the sub-linear expectation are established.As an application of the maximal inequalities,the sufficient and necessary conditions for the central limit theorem of independent and identically distributed random variables are also obtained.     

Generalized multiresolution structures in reducing subspaces of L 2(ℝ d )

In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.     

AN INVERSE EIGENVALUE PROBLEM FOR JACOBI MATRICES

In this paper, we discuss an inverse eigenvalue problem for constructing a 2n × 2n Jacobi matrix T such that its 2n eigenvalues are given distinct real values and its leading principal submatrix of order n is a given Jacobi matrix. A new sufficient and necessary condition for the solvability of the above problem is given in this paper. Furthermore, we present a new algorithm and give some numerical results.     

Spectral gap and convergence rate for discrete-time Markov chains

Let P be a transition matrix which is symmetric with respect to a measure π.The spectral gap of P in L2(π)-space,denoted by gap(P),is defined as the distance between 1 and the rest of the spectrum of P.In this paper,we study the relationship between gap(P) and the convergence rate of Pn.When P is transient,the convergence rate of P n is equal to 1 gap(P).When P is ergodic,we give the explicit upper and lower bounds for the convergence rate of Pn in terms of gap(P).These results are extended to L∞(π)-space.     

SIGN MATRIX, REGULAR SPLITTINGS AND MONOTONIC ENCLOSURE OF SOLUTIONS FOR NONLINEAR SYSTEM OF EQUATIONS, PARTI

In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.     

QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation modelwhere 0   

On Two-stage Estimate Based on Independent Estimate of Covariance Matrix

When an independent estimate of covariance matrix is available, we often prefer two-stage estimate （TSE）. Expressions of exact covarianee matrix of the TSE obtained by using all and some covariables in eovariance adjustment approach are given, and a necessary and sufficient condition for the TSE to be superior to the least square estimate and related large sample test is also established. Furthermore the TSE, by using some covariables, is expressed as weighted least square estimate. Basing on this fact, a necessary and sufficient condition for the TSE by using some covariables to be superior to the TSE by using all eovariables is obtained. These results give us some insight into the selection of covariables in the TSE and its application.     

The Limit Behaviour of Imprecise Continuous-Time Markov Chains

We study the limit behaviour of a nonlinear differential equation whose solution is a superadditive generalisation of a stochastic matrix, prove convergence, and provide necessary and sufficient conditions for ergodicity. In the linear case, the solution of our differential equation is equal to the matrix exponential of an intensity matrix and can then be interpreted as the transition operator of a homogeneous continuous-time Markov chain. Similarly, in the generalised nonlinear case that we consider, the solution can be interpreted as the lower transition operator of a specific set of non-homogeneous continuous-time Markov chains, called an imprecise continuous-time Markov chain. In this context, our convergence result shows that for a fixed initial state, an imprecise continuous-time Markov chain always converges to a limiting distribution, and our ergodicity result provides a necessary and sufficient condition for this limiting distribution to be independent of the initial state.     

Convergence and quotient convergence of iterative methods for solving singular linear equations with index one

Singular systems with index one arise in many applications, such as Markov chain modelling. In this paper, we use the group inverse to characterize the convergence and quotient convergence properties of stationary iterative schemes for solving consistent singular linear systems when the index of the coefficient matrix equals one. We give necessary and sufficient conditions for the convergence of stationary iterative methods for such problems. Next we show that for the stationary iterative method, the convergence and the quotient convergence are equivalent.     

Convergence of a Penalty Method for Mathematical Programming with Complementarity Constraints

We adapt the convergence analysis of the smoothing (Ref. 1) and regularization (Ref. 2) methods to a penalty framework for mathematical programs with complementarity constraints (MPCC); we show that the penalty framework shares convergence properties similar to those of these methods. Moreover, we give sufficient conditions for a sequence generated by the penalty framework to be attracted to a B-stationary point of the MPCC.     

契比雪夫半迭代法的收敛性

其中,G是一个依赖于A的N阶矩阵,h是一个依赖于A和b的N阶向量。 方法(2)收敛的充要条件是迭代矩阵G的谱半径小于1。这个结论适合于任一线性定常迭代方法。但对非定常迭代方法,收敛性问题比较复杂,一般很难运用谱半径进行收敛性分析,Young给出的一个例子(见[1pp.298])便说明了这一点。 然而,对一种特殊的非定常迭代方法——契比雪夫半迭代法(下文简称CSI方法),却可以提供基于谱半径的收敛性条件。这正是本文的核心内容。     

A study on the convergence of homotopy analysis method

In this study, a reliable approach for convergence of the homotopy analysis method when applied to nonlinear problems is discussed. First, we present an alternative framework of the method which can be used simply and effectively to handle nonlinear problems. Then, mainly, we address the sufficient condition for convergence of the method. The convergence analysis is reliable enough to estimate the maximum absolute truncated error of the homotopy series solution. The analysis is illustrated by investigating the convergence results for some nonlinear differential equations. The study highlights the power of the method.     

A necessary and sufficient convergence condition of orthomin(k) methods for least squares problem with weight

A class of Orthomin-type methods for linear systems based on conjugate residuals is extended to a form suitable for solving a least squares problem with weight. In these algorithms a mapping matrix as preconditioner is brought into use. We also give a necessary and sufficient condition for the convergence of the algorithm. Furthermore, we also study the construction of the mapping matrix for which the necessary and sufficient condition holds.     

正项矩阵级数的敛散性研究

本文研究了正项矩阵级数收敛的充要条件 ,从而把正项级数的收敛原理推广到了正项矩阵级数的情形 .     

Convergence of matrix continued fractions

The aim of this work is to give some criteria on the convergence of matrix continued fractions. We begin by presenting some new results which generalize the links between the convergent elements of real continued fractions. Secondly, we give necessary and sufficient conditions for the convergence of continued fractions of matrix arguments. This paper will be completed by illustrating the theoretical results with some examples.     

Convergence of the parallel chaotic waveform relaxation method for stiff systems

In this paper, we establish several algorithms for parallel chaotic waveform relaxation methods for solving linear ordinary differential systems based on some given models. Under some different assumptions on the coefficient matrix A and its multisplittings we obtain corresponding sufficient conditions of convergence of the algorithms. Also a discussion on convergence speed comparison of synchronous and asynchronous algorithms is given.     

Positivity of linear transformations of mean-starshaped sequences

In this paper, we give the necessary and sufficient conditions for a linear transformation of a mean-starshaped sequence to be positive. Using this result, we obtain the necessary and sufficient conditions for a lower triangular matrix to preserve the mean-starshape of a sequence and we discuss some special cases of linear transformations. Our next result deals with the convergence of a sequence of mean-starshaped sequences to any given mean-starshaped sequence and the positivity of a linear operator on the set of mean-starshaped sequences.