New band Toeplitz preconditioners for ill-conditioned symmetric positive definite Toeplitz systems
| dc.contributor.author | Noutsos, D. | en |
| dc.contributor.author | Vassalos, P. | en |
| dc.date.accessioned | 2015-11-24T17:25:44Z | |
| dc.date.available | 2015-11-24T17:25:44Z | |
| dc.identifier.issn | 0895-4798 | - |
| dc.identifier.uri | https://olympias.lib.uoi.gr/jspui/handle/123456789/13089 | |
| dc.rights | Default Licence | - |
| dc.subject | low rank correction | en |
| dc.subject | toeplitz matrix | en |
| dc.subject | conjugate gradient | en |
| dc.subject | rational interpolation and approximation | en |
| dc.subject | preconditioner | en |
| dc.subject | matrices | en |
| dc.title | New band Toeplitz preconditioners for ill-conditioned symmetric positive definite Toeplitz systems | en |
| heal.abstract | It is well known that preconditioned conjugate gradient (PCG) methods are widely used to solve ill-conditioned Toeplitz linear systems T-n(f)x = b. In this paper we present a new preconditioning technique for the solution of symmetric Toeplitz systems generated by nonnegative functions f with zeros of even order. More specifically, f is divided by the appropriate trigonometric polynomial g of the smallest degree, with zeros the zeros of f, to eliminate its zeros. Using rational approximation we approximate rootf/g by p/q, p, q trigonometric polynomials and consider p(2)g/q(2) as a very satisfactory approximation of f. We propose the matrix M-n = B-n(-1)(q)B-n(p(2)g)B-n(-1)(q), where B (.) denotes the associated band Toeplitz matrix, as a preconditioner whence a good clustering of the spectrum of its preconditioned matrix is obtained. We also show that the proposed technique can be very flexible, a fact that is confirmed by various numerical experiments so that in many cases it constitutes a much more efficient strategy than the existing ones. | en |
| heal.access | campus | - |
| heal.fullTextAvailability | TRUE | - |
| heal.identifier.secondary | <Go to ISI>://000174378500009 | - |
| heal.journalName | Siam Journal on Matrix Analysis and Applications | en |
| heal.journalType | peer reviewed | - |
| heal.language | en | - |
| heal.publicationDate | 2002 | - |
| heal.publisher | Society for Industrial and Applied Mathematics | en |
| heal.recordProvider | Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών | el |
| heal.type | journalArticle | - |
| heal.type.el | Άρθρο Περιοδικού | el |
| heal.type.en | Journal article | en |
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