On block matrices associated with discrete Trigonometric transforms and their use in the theory of wave propagation

Tsitsas, N-L

dc.contributor.author	Tsitsas, N-L	en
dc.date.accessioned	2014-03-01T01:34:00Z
dc.date.available	2014-03-01T01:34:00Z
dc.date.issued	2010	en
dc.identifier.issn	0254-9409	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20639
dc.subject	Block matrices	en
dc.subject	Discrete Trigonometric transforms	en
dc.subject	Efficient inversion algorithms	en
dc.subject	Numerical methods in wave propagation theory	en
dc.subject	Wave radiation and scattering	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mathematics	en
dc.subject.other	AUXILIARY SOURCES MAS	en
dc.subject.other	OBLIQUE-INCIDENCE	en
dc.subject.other	SMALL-VOLUME	en
dc.subject.other	SCATTERING	en
dc.subject.other	ALGORITHMS	en
dc.subject.other	OPTIMIZATION	en
dc.subject.other	CYLINDER	en
dc.subject.other	COSINE	en
dc.title	On block matrices associated with discrete Trigonometric transforms and their use in the theory of wave propagation	en
heal.type	journalArticle	en
heal.identifier.primary	10.4208/jcm.l004-m3193	en
heal.identifier.secondary	http://dx.doi.org/10.4208/jcm.l004-m3193	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	Block matrices associated with discrete Trigonometric transforms (DTT's) arise in the mathematical modelling of several applications of wave propagation theory including discretizations of scatterers and radiators with the Method of Moments, the Boundary Element Method, and the Method of Auxiliary Sources. The DTT's are represented by the Fourier, Hartley, Cosine, and Sine matrices, which are unitary and offer simultaneous diagonalizations of specific matrix algebras. The main tool for the investigation of the aforementioned wave applications is the efficient inversion of such types of block matrices. To this direction, in this paper we develop an efficient algorithm for the inversion of matrices with U-diagonalizable blocks (U a fixed unitary matrix) by utilizing the U-diagonalization of each block and subsequently a similarity transformation procedure. We determine the developed method's computational complexity and point out its high efficiency compared to standard inversion techniques. An implementation of the algorithm in Matlab is given. Several numerical results are presented demonstrating the CPU-time efficiency and accuracy for ill-conditioned matrices of the method. The investigated matrices stem from real-world wave propagation applications. © Copyright 2010 by AMSS, Chinese Academy of Sciences.	en
heal.publisher	VSP BV	en
heal.journalName	Journal of Computational Mathematics	en
dc.identifier.doi	10.4208/jcm.l004-m3193	en
dc.identifier.isi	ISI:000286949300009	en
dc.identifier.volume	28	en
dc.identifier.issue	6	en
dc.identifier.spage	864	en
dc.identifier.epage	878	en