A study of Vandermonde-like matrix systems with emphasis on preconditioning and Krylov matrix connection
Year: 2009
Type: dissertation
Abstract: The study focuses primarily on Vandermonde-like matrix systems. The idea is to express Vandermonde and Vandermonde-like matrix systems as the problems related to Krylov Matrices. The connection provides a different angle to view the Vandermonde-like systems. Krylov subspace methods are strongly related to polynomial spaces, hence a nice connection can be established using LU factorization as proposed by Bjorck and Pereyra and QR factorization by Reichel. Further an algorithm to generate a preconditioner is incorporated in GR algorithm given by Reichel . This generates a preconditioner for Vandermonde-like matrices consisting of polynomials which obey a three term recurrence relation. This general preconditioner works effectively for Vandermonde matrices as well. The preconditioner is then tested on various distinct nodes. Based on results obtained, it is established that the condition number of Vandermonde -like matrices can be lowered significantly by application of the preconditioner, for some cases.
Author: Jyoti Saraswat
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W132233568