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New Square-Root Factorization of Inverse Toeplitz Matrices
KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. (System Identification Group)ORCID iD: 0000-0002-1927-1690
Uppsala University.
2010 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 17, no 2, 137-140 p.Article in journal (Refereed) Published
Abstract [en]

Square-root (in particular, Cholesky) factorization of Toeplitz matrices and of their inverses is a classical area of research. The Schur algorithm yields directly the Cholesky factorization of a symmetric Toeplitz matrix, whereas the Levinson algorithm does the same for the inverse matrix. The objective of this letter is to use results from the theory of rational orthonormal functions to derive square-root factorizations of the inverse of an positive definite Toeplitz matrix. The main result is a new factorization based on the Takenaka-Malmquist functions, that is parameterized by the roots of the corresponding auto-regressive polynomial of order. We will also discuss briefly the connection between our analysis and some classical results such as Schur polynomials and the Gohberg-Semencul inversion formula.

Place, publisher, year, edition, pages
IEEE , 2010. Vol. 17, no 2, 137-140 p.
Keyword [en]
AR processes, rational orthonormal functions, square-root and Cholesky, factorization, Toeplitz matrix
National Category
Control Engineering
URN: urn:nbn:se:kth:diva-18964DOI: 10.1109/lsp.2009.2035372ISI: 000271838400004ScopusID: 2-s2.0-80052317463OAI: diva2:337011
© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20120120Available from: 2012-01-20 Created: 2010-08-05 Last updated: 2013-09-05Bibliographically approved

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