A Study of Vandermonde-like Matrix Systems With Emphasis on Preconditioning and Krylov Matrix Connection.
Issue Date
2009-06-11Author
Saraswat, Jyoti
Publisher
University of Kansas
Format
88 pages
Type
Thesis
Degree Level
M.A.
Discipline
Mathematics
Rights
This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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Show full item recordAbstract
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.
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- Mathematics Dissertations and Theses [179]
- Theses [3901]
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