Towards a Lanczos' -Method Toolkit for Differential Problems

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Trindade, M (Author) Other; Matos, J (Author) Other; Vasconcelos, PB (Author) FEP

Journal

Title: Mathematics in Computer Science

Vol. 10 No. 3

Pages: 313-329

ISSN: 1661-8270

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 5 Citations

Other information

Authenticus ID: P-00K-EAB

DOI: 10.1007/s11786-016-0269-x

Abstract (EN): The aim of this work is to build a numerical software library based on the -method to solve differential problems using MATLAB. The -method can be very effective in the solution of certain type of these problems, and therefore, the existence of a numerical library for its dissemination is of major importance. Furthermore, the method has been used for the solution of particular problems but has not yet been explored as a general technique. Focus will be on stability issues, namely those issued from the solution of algebraic linear systems required for the process. Additionally, preconditioners for the solution with the -method will be tackled, with emphasizes on incomplete LU factorizations and (block) Jacobi preconditioners. We also propose an iterative approach, build upon an LU factorization over a moderate initial size, generating better approximations and providing a priori error estimate at each iteration. Numerical results enlightening the efficiency of the proposed methods will be presented.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17