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.
翻译:在这一论文中,研究了三类不同问题的数字解决办法,具体地说,提出了新的技术,并进行了理论分析,同时进行了一系列广泛的数字实验,以进一步调查并比较所提出的方法的有效性和性能,前两项属于数字线性代数研究领域,涉及大型结构直线系统系数矩阵的光谱分析和Krylov子空间方法的先决条件,第三项涉及金融计算领域的一个问题,即美国组合选项的定价问题。