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A method of matrix inverse triangular decomposition based on contiguous principal submatrices. (English) Zbl 0438.65033


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
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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
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