Spectral Analysis and Preconditioned Iterative Solvers for Large Structured Linear Systems

TL;DR

This thesis explores spectral analysis and preconditioning techniques for large structured linear systems, enhancing iterative solver efficiency, and applies these methods to financial option pricing problems.

Contribution

It introduces new spectral analysis and preconditioning methods for Krylov subspace solvers tailored to structured linear systems, with theoretical validation and numerical experiments.

Findings

Improved convergence rates for Krylov methods with new preconditioners

Enhanced spectral understanding of structured matrices

Effective application to American put option pricing

Abstract

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.