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On the optimal complex extrapolation of the complex Cayley transform
dc.creator | Hadjidimos, A. | en |
dc.creator | Tzoumas, M. | en |
dc.date.accessioned | 2015-11-23T10:29:21Z | |
dc.date.available | 2015-11-23T10:29:21Z | |
dc.date.issued | 2009 | |
dc.identifier | 10.1016/j.laa.2008.08.010 | |
dc.identifier.issn | 0024-3795 | |
dc.identifier.uri | http://hdl.handle.net/11615/28273 | |
dc.description.abstract | The Cayley transform, F := F(A) = (I + A)(-1) (I - A), with A epsilon C(n.n) and -1 is not an element of sigma (A), where sigma(.) denotes spectrum, and its extrapolated counterpart F (omega A), omega epsilon C\{0} and -1 is not an element of sigma (omega A), are of significant theoretical and practical importance (see, e.g. [A. Hadjidimos, M. Tzoumas, On the principle of extrapolation and the Cayley transform, Linear Algebra Appl., in press]). In this work, we extend the theory in [8] to cover the complex case. Specifically, we determine the optimal extrapolation parameter omega epsilon C\{0} for which the spectral radius of the extrapolated Cayley transform rho(F(omega A)) is minimized assuming that sigma(A) subset of H, where H is the smallest closed convex polygon, and satisfies O(0) is not an element of H. As an application, we show how a complex linear system, with coefficient a certain class of indefinite matrices, which the ADI-type method of Hermitian/Skew-Hermitian splitting fails to solve, can be solved in a "best" way by the aforementioned method. (C) 2008 Elsevier Inc. All rights reserved. | en |
dc.source.uri | <Go to ISI>://WOS:000261547100003 | |
dc.subject | Cayley transform | en |
dc.subject | Extrapolation | en |
dc.subject | Convex hull | en |
dc.subject | Mobius transformation | en |
dc.subject | Capturing circle | en |
dc.subject | Visibility angle | en |
dc.subject | Hermitian/Skew-Hermitian splitting | en |
dc.subject | ITERATION | en |
dc.subject | SCHEME | en |
dc.subject | Mathematics, Applied | en |
dc.subject | Mathematics | en |
dc.title | On the optimal complex extrapolation of the complex Cayley transform | en |
dc.type | journalArticle | en |
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