A method of matrix inverse triangular decomposition based on contiguous principal submatrices

DOI10.1016/0024-3795(80)90219-0zbMath0438.65033OpenAlexW2056480844MaRDI QIDQ1142008

Y. Kamp, Y. Genin, Philippe Delsarte

Publication date: 1980

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(80)90219-0

zbMATH Keywords

computational complexityToeplitz matricestriangular decompositionHermitian Toeplitz matricesprincipal submatricesalgorithm of Levinson-Trench

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Hermitian, skew-Hermitian, and related matrices (15B57) Direct numerical methods for linear systems and matrix inversion (65F05) Algorithms in computer science (68W99)

Related Items (6)

Characterization of the partial autocorrelation function of nonstationary time series. ⋮ Covariance decompositions via elementary transformations. Applications to filtering ⋮ From Bareiss' algorithm to the stable computation of partial correlations ⋮ Two composition methods for solving certain systems of linear equations ⋮ Parallel solution of symmetric positive definite systems with hyperbolic rotations ⋮ Maximum of entropy and extension of covariance matrices for periodically correlated and multivariate processes.

Cites Work

• Displacement ranks of matrices and linear equations
• Half-plane Toeplitz systems
• A view of three decades of linear filtering theory
• Inverses of Toeplitz Operators, Innovations, and Orthogonal Polynomials
• Design of two-dimensional semicasual recursive filters
• On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix
• An Algorithm for the Inversion of Finite Toeplitz Matrices
• Toeplitz Matrix Inversion: The Algorithm of W. F. Trench

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