标题： 谱分析和预处理迭代求解器在大型结构化线性方程组中的应用 显示英文标题

标题： Spectral Analysis and Preconditioned Iterative Solvers for Large Structured Linear Systems

摘要： 在本论文中，研究了三类不同问题的数值解法。 具体来说，提出了新的技术并进行了理论分析，同时进行了一套广泛的数值实验，以进一步研究并比较所提出方法的有效性和性能。 前两个属于数值线性代数的研究领域，涉及大型结构化线性系统系数矩阵的Krylov子空间方法的谱分析和预处理。 第三个问题来自金融计算领域，即美式看跌期权的定价。 显示英文摘要

摘要： In this thesis, the numerical solution of three different classes of problems have been studied. Specifically, new techniques have been proposed and their theoretical analysis has been performed, accompanied by a wide set of numerical experiments, for investigating further and comparing the effectiveness and performance of the presented approach. The first two belong to the research area of numerical linear algebra and concern the spectral analysis and preconditioning for Krylov subspace methods of the coefficient matrix of large structured linear systems. The third concerns a problem from the area of financial computing namely the pricing of an American put option.