Delsarte, Ph.; Genin, Y.; Kamp, Y. A method of matrix inverse triangular decomposition based on contiguous principal submatrices. (English) Zbl 0438.65033 Linear Algebra Appl. 31, 199-212 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 6 Documents MSC: 65F05 Direct numerical methods for linear systems and matrix inversion 15B57 Hermitian, skew-Hermitian, and related matrices 15A09 Theory of matrix inversion and generalized inverses 15A23 Factorization of matrices 68W99 Algorithms in computer science 68Q25 Analysis of algorithms and problem complexity Keywords:triangular decomposition; principal submatrices; computational complexity; Toeplitz matrices; Hermitian Toeplitz matrices; algorithm of Levinson-Trench PDFBibTeX XMLCite \textit{Ph. Delsarte} et al., Linear Algebra Appl. 31, 199--212 (1980; Zbl 0438.65033) Full Text: DOI References: [1] Chang, H.; Aggarwal, J. K., Design of two-dimensional semicausal recursive digital filters, IEEE Trans. Circuits and Systems, CAS-25, 1051-1059 (1978) · Zbl 0401.93043 [2] P. Delsarte, Y. Genin, and Y. Kamp, Half-plane Toeplitz systems, IEEE Trans.Information Theory; P. Delsarte, Y. Genin, and Y. Kamp, Half-plane Toeplitz systems, IEEE Trans.Information Theory · Zbl 0439.41029 [3] Justice, J. H., A Levinson-type algorithm for two-dimensional Wiener filtering using bivariate Szegö polynomials, Proc. IEEE, 65, 882-886 (1977) [4] Kailath, T., A view of three decades of linear filtering theory, IEEE Trans. Information Theory, IT-20, 146-181 (1974) · Zbl 0307.93040 [5] Kailath, T.; Kung, S-Y.; Morf, M., Displacement ranks of matrices and linear equations, J. Math. Anal. Appl., 68, 395-407 (1979) · Zbl 0433.15001 [6] Kailath, T.; Vieira, A.; Morf, M., Inverses of Toeplitz operators, innovations and orthogonal polynomials, SIAM Rev., 20, 106-119 (1978) · Zbl 0382.47013 [7] Levinson, N., The Wiener rms (root-mean-square) error criterion in filter design and prediction, J. Math. and Phys., 25, 261-278 (1946) [8] Trench, W. F., An algorithm for the inversion of finite Toeplitz matrices, J. SIAM, 12, 515-522 (1964) · Zbl 0131.36002 [9] Whittle, P., On the fitting of multivariate autoregressions and the approximate canonical factorization of a spectral density matrix, Biometrika, 50, 129-134 (1963) · Zbl 0129.11304 [10] Wiggins, R. A.; Robinson, E. A., Recursive solution to the multichannel filtering problem, J. Geophys. Res., 70, 1885-1891 (1965) [11] Zohar, S., Toeplitz matrix inversion: the algorithm of W.F. Trench, J. Assoc. Comput. Mach., 16, 592-601 (1969) · Zbl 0194.18102 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.