Your browser does not support JavaScript!

Post-graduate theses

Current Record: 4 of 123

Back to Results Previous page
Next page
Add to Basket
[Add to Basket]
Identifier 000457234
Title Direct and iterative methods for large sparse linear systems
Alternative Title Άμεσες και επαναληπτικές μέθοδοι για μεγάλα αραιά γραμμικά συστήματα
Author Χατζηχαμπή, Νικολέττα
Thesis advisor Πλεξουσάκης, Μιχαήλ
Reviewer Κατσαούνης, Θεόδωρος
Χατζηπαντελίδης, Παναγιώτης
Abstract In this thesis presented an overview of direct and iterative methods for solving large sparse linear systems such as Ax = b where A ∈ Cn×n and b ∈ Cn. In numerical analysis and scientific computing, an important condition for the computations is the low consuming of memory storage. A sparse linear system has the advantage that the amount of storage required is greatly reduced and several storage schemes have been devised for this special category. The respective theory was developed in the second chapter. In addition, the computational cost is reduced since we know beforehand the result of arithmetic operations with zero. The main challenge in sparse linear algebra is to balance storage, computational cost and stability to create an effective solution. In chapter 2, it is also described the Finite Difference Methods, a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Later in chapter 3, there are developed the Stationary Iterative Methods. Some of them are the well– known methods of Jacobi, Gauss–Seidel and SOR method as well. Consequently, we emphasize the linear iterative schemes that constitute an important part of iterative methods. Continuing into Chapter 4, we define the Krylov subspace. The jth Krylov subspace formed by the linear combination of b,Ab, · · · ,Aj−ib and comprises the base of Gradient methods. We will refer to the steepest descent method and the conjugate gradient method which differ in the search direction. Finally, in Chapter 5 we present the results of numerical experiments performed with the solution of linear systems which result from the discretization of the Helmholtz equation, using finite difference and finite element methods. The Python codes used in the numerical experiments performed in this thesis are listed in Appendix A.
Language English
Issue date 2023-07-21
Collection   School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
Permanent Link https://elocus.lib.uoc.gr//dlib/e/3/7/metadata-dlib-1689246447-343274-31167.tkl Bookmark and Share
Views 398

Digital Documents
No preview available

Download document
View document
Views : 0