计算流队列中出现的大型块三角块托普利茨矩阵的指数

Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices

In this work we study the convergence properties of the one-level parallel Schwarz method with Robin transmission conditions applied to the one-dimensional and two-dimensional Helmholtz and Maxwell's equations. One-level methods are not scalable in general. However, it has recently been proven that when impedance transmission conditions are used in the case of the algorithm applied to the equations with absorption, under certain assumptions, scalability can be achieved and no coarse space is required. We show here that this result is also true for the iterative version of the method at the con…

Solving quadratic matrix equations arising in random walks in the quarter plane

Quadratic matrix equations of the kind $A_1X^2+A_0X+A_{-1}=X$ are encountered in the analysis of Quasi--Birth-Death stochastic processes where the solution of interest is the minimal nonnegative solution $G$. In many queueing models, described by random walks in the quarter plane, the coefficients $A_1,A_0,A_{-1}$ are infinite tridiagonal matrices with an almost Toeplitz structure. Here, we analyze some fixed point iterations, including Newton's iteration, for the computation of $G$ and introduce effective algorithms and acceleration strategies which fully exploit the Toeplitz structure of the…

结构矩阵partial pivoting方法的误差分析

Error analysis of a partial pivoting method for structured matrices

在信号处理问题的解中出现的许多矩阵具有特殊的位移结构。例如，自适应滤波和到达方向估计产生Toeplitz类型的矩阵。Gohberg，Kailath和Olshevsky（GKO）最近的方法允许快速高斯消去法与部分旋转这样的结构矩阵。在本文中，舍入误差分析进行的柯西和Toeplitz变种的GKO方法。它示出的误差增长取决于某些辅助向量，生成元，这是由GKO算法计算的增长。它还表明，在某些情况下，在发电机的增长可以是大的，所以误差的增长是远远大于将遇到正常的高斯消去法与部分枢轴。提出了一种改进的算法来执行一种类型的行列旋转，它可以改善这个问题。

半无限准Toeplitz矩阵及其在QBD随机过程中的应用

Semi-Infinite Quasi-Toeplitz Matrices with Applications to QBD Stochastic Processes

本文研究了半无限准Toeplitz矩阵的性质，并提出了一种有限表示方法和相关算法，用于解决涉及可数相态的Quasi-Birth and Death (QBD)随机过程的二次矩阵方程。