双对称非负定阵一类逆特征值问题的最小二乘解

１．引言 逆特征值问题在工程中有广泛的应用，其研究已有一些很好的结果［１－５］．最近，文［６］还研究了双对称矩阵逆特征值问题，即研究了如下两个问题： 问题Ａ．已知Ｘ∈Ｒｎｘｍ，Ａ＝ｄｉａｇ（λ１…，λｍ），求Ａ∈ＢＳＲｎｘｎ使 ＡＸ＝ＸＡ，其中 Ｒｎｘｍ表示全体 ｎ ｘ ｍ实矩阵集合， ＢＳＲｎｘｎ表示全体 ｎ ｘ ｎ双对称阵集合． 问题Ｂ．已知Ａ＊ＥＲｎｘｎ，求Ａ∈ＳＥ使 ｜｜Ａ＊－Ａ｜｜＝ ｉｎｆ ｜｜Ａ＊－Ａ｜｜ ＡＦＳＥ其中 ＳＥ是问题 Ａ的解集合，｜｜． ｜｜表示 Ｆｒｏｂｅｎｉｕｓ范数． 在实际问题中， …  

具有参数的不带有导数的平方收敛的迭代法

1.引 言 考虑数值求解非线性方程 f(x)=0, (1)其中实值函数f(x)在实零点x*的某邻域U(x*)内连续可微且f'(x)≠0. 牛顿法是科学与工程计算中数值求解(1)的常用数值方法.虽然它一般至少是二阶收敛的,但它需要调用导数值,这使其应用受到限制.我们修改牛顿法,用割线代替切线可得不带  

Newton-Thiele's rational interpolants

It is well known that Newton's interpolation polynomial is based on divided differences which produce useful intermediate results and allow one to compute the polynomial recursively. Thiele's interpolating continued fraction is aimed at building a rational function which interpolates the given support points. It is interesting to notice that Newton's interpolation polynomials and Thiele's interpolating continued fractions can be incorporated in tensor‐product‐like manner to yield four kinds of bivariate interpolation schemes. Among them are classical bivariate Newton's interpolation polynomials which are purely linear interpolants, branched continued fractions which are purely nonlinear interpolants and have been studied by Chaffy, Cuyt and Verdonk, Kuchminska, Siemaszko and many other authors, and Thiele-Newton's bivariate interpolating continued fractions which are investigated in another paper by one of the authors. In this paper, emphasis is put on the study of Newton-Thiele's bivariate rational interpolants. By introducing so‐called blending differences which look partially like divided differences and partially like inverse differences, we give a recursive algorithm accompanied with a numerical example. Moreover, we bring out the error estimation and discuss the limiting case. This revised version was published online in June 2006 with corrections to the Cover Date.  

Sensitivity Analysis for Quasi-Variational Inequalities

In this paper, we develop a sensitivity analysis framework for quasi-variational inequalities using the Wiener–Hopf equations technique without assuming the differentiability of the given data.  

一类具有连续分布的偏差变元的双曲型方程的振动准则

本文研究了连续分布偏差变元的双曲型方程，利用化多维振动问题为一维问题的方法，得到了某些边值问题的每一个解均为振动的充分条件。所得条件推广和改进了文献中的结果。  

层次分析积因子位次赋值数据求权重研究

本文针对传统的层次分析法，提出了一种改进的积因子方法，采用算术平均数赋值方法代替专家打分，最大程度上避免了主观判断可能造成的决策失误。并结合实际问题进行计算，得到了符合实际的结果。  

一种改进的模拟退火算法

1 引言 在过去的几十年中，最优化的任务在诸如以下不同领域中表现为稳步上升趋势，如电子工程、操作系统、计算机科学和通信等，其中的NP完全问题不易得出最优解，它被所解问题大小的一个多项式函数所限制，且其求解时间随问题规模呈指数级增长，当规模稍大时就会因时间限制而失去可行性。  

伽玛分布参数的最短置信区间

Γ(β,θ)分布中未知参数θ的最短置信区间实际上是一个条件极值问题,它能转化成一个方程组可用数值方法迭代求解。在假设参数β=1,置信水平为0.95的条件下,比较了常用置信区间与最短置信区间的长度,结果表明:两者长度的绝对差d(n)和相对差e(n)均随样本容量n的增大而减小,当n≤9时,e(n)≥10%。这说明在小样本下,研究参数的最短置信区间是必要的。  

一个具有时滞和阶段结构的捕食-被捕食模型

研究一个具有时滞和阶段结构的捕食者-食饵模型.通过构造适当的Lyapunov泛函,讨论了该模型的正平衡点和非负边界平衡点的全局吸引性,从而得到了保证该生态系统永久持续生存与绝灭的充分性条件.