GPSD迭代法和Jacobi迭代法的敛散关系

证明了当Jacobi迭代矩阵B非负时,解线性方程组Ax=b(A为不可约矩阵)的GPSD迭代法(0＜ωi＜Ti≤1,i=1,2,…,n)和Jacobi迭代法同时敛散,给出了其谱半径p(ST,Ω)和ρ(B)之间的关系.     

MPSD迭代法和Jacobi迭代法的敛散关系

本文证明了当Jacobi迭代矩阵B非负时,解线性方程组Ax=b(A为不可约矩阵)的MPSD迭代法(0＜wi＜τ≤1,i=1,2)和Jacobi迭代法同时敛散,给出了其谱半径ρ(Sτ,w1,w2)和ρ(B)之间的关系.     

GAOR迭代法收敛判别准则

本文将文「１」中给出的判别超松驰（即ＳＯＲ）迭代法的一个收敛性准则推广到ＧＡＯＲ迭代法，并且去掉了Ａ为不可约矩阵或／ａｉｉ／＋ｕｉ〉０（ｉ＝１，２，…，ｎ）这一条件，本文的结果所涉及的和收敛范围，均扩广交包含了文「１」中的定理。     

TOR,GAOR和GSAOR迭代法收敛准则

熟知,解线性方程组的TOR迭代法包括了Jacobi,Gauss-Seidel,SOR,AOR等迭代法.而GAOR和GSAOR迭代法则包括了GSOR,SSOR,SAOR,GSSOR和MSOR等迭代法。 本文给出了一些新的,易于检验的迭代法收敛准则,它能用来判别一类矩阵A之Jacobi矩阵B=I-D~(-1)A(或矩阵B=I-AD~(-1))的模B≥1,以及A为(行或列)弱对角占优矩阵     

GAOR迭代法的收敛性

当A为实对称矩阵时,[1]中在D_i选取较特殊的条件下,证明了GAOR迭代法收敛的充要条件为A是正定矩阵. 设A为Hermite矩阵,进一步讨论GAOR迭代法收敛的充要条件. 以下记 B=D_1~(-1)(C_L+C_U).     

Jacobi,Gauss—Seidel迭代法收敛准则的改进

本文改进了文[1]的Jacobi和Gauss-Seidel迭代法收敛和发散判别准则。     

基于P级数判敛的正项级数敛散性判别方法

借助由比较判别法导出的引理,证明了一种形式类同比值判别法的新的判别方法。     

一个不等式在判别级数敛散性方面的应用

讨论一个不等式在幂级数和一些常数项级数敛散性判定中的应用.     

交错级数敛散性判别法

给出交错级数的几个判别法,它们可直接用以判别交错级数是绝对收敛,条件收敛还是发散.     

解线性区间方程组的并行多分裂GAOR方法

本文引入区间三角多分裂来包含集合Ｓ＝｛Ａ－１ｂ｜Ａ∈Ｅ［Ａ］，ｂ∈［ｂ］｝，给出解区间线性方程组的并行多分裂ＧＡＯＲ方法，讨论方法的收敛性、收敛速度以及其极限包含集合Ｓ的性质．     

两种反常积分敛散性的判别方法

介绍了两种判别反常积分敛散性的判别方法.     

Convergence of GAOR method for doubly diagonally dominant matrices

In this paper, we obtain bounds for the spectral radius of the matrix l_ω,r which is the iterative matrix of the generalized accelerated overrelaxation (GAOR) iterative method. Moreover, we present one convergence theorem of the GAOR method. Finally, we present two numerical examples.     

Uniform Convergence of Fourier–Jacobi Series

Necessary and sufficient conditions which imply the uniform convergence of the Fourier–Jacobi series of a continuous function are obtained under an assumption that the Fourier–Jacobi series is convergent at the end points of the segment of orthogonality [−1,1]. The conditions are in terms of the modulus of continuity, Λ-variation, and the modulus of variation of a function.     

几类级数敛散性的一些探讨

通过对子级数的探讨,得到了一类级数和其子级数的敛散性的判断准则.与此同时,对文[3]的结论进行了推广.     

Convergence analysis of Jacobi spectral collocation methods for Abel-Volterra integral equations of second kind

This work is to analyze a spectral Jacobi-collocation approximation for Volterra integral equations with singular kernel ϕ(t, s) = (t − s)^−μ. In an earlier work of Y. Chen and T. Tang [J. Comput. Appl. Math., 2009, 233: 938–950], the error analysis for this approach is carried out for 0 < μ < 1/2 under the assumption that the underlying solution is smooth. It is noted that there is a technical problem to extend the result to the case of Abel-type, i.e., μ = 1/2. In this work, we will not only extend the convergence analysis by Chen and Tang to the Abel-type but also establish the error estimates under a more general regularity assumption on the exact solution.     

判定级数敛散性的两种初等方法

借助实例介绍针对某类级数敛散性的两种初等判定方法,即由级数通项构造相关不等式后运用比较判别法,或对级数恒等变换后再进行拆项求和.