Matrices with banded inverses: inversion algorithms and factorization of Gauss-Markov processes

DOI10.1109/18.954748zbMath0998.65037OpenAlexW2151757774MaRDI QIDQ4501738

Aleksandar Kavčić, José M. F. Moura

Publication date: 7 September 2000

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/18.954748

zbMATH Keywords

Hadamard productcovariance matrixtridiagonal matrixmatrix inversionKullback-Leibler distanceCholesky decompositionGauss-Markov processespotential matrixbanded matrixmaximum-entropy method\(L\)-band complementinhomogeneous autoregressive processesnested inversion algorithm

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Discrete-time Markov processes on general state spaces (60J05) Numerical analysis or methods applied to Markov chains (65C40) Analysis of variance and covariance (ANOVA) (62J10) Direct numerical methods for linear systems and matrix inversion (65F05)

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Characterizations and accurate computations for tridiagonal Toeplitz matrices ⋮ Gaussian and robust Kronecker product covariance estimation: existence and uniqueness ⋮ An L-Banded Approximation to the Inverse of Symmetric Toeplitz Matrices ⋮ Matrices whose inverses are tridiagonal, band or block-tridiagonal and their relationship with the covariance matrices of a random Markov process ⋮ Limited memory BFGS method for least squares semidefinite programming with banded structure ⋮ Graph signal processing on dynamic graphs based on temporal-attention product ⋮ An MSSS-preconditioned matrix equation approach for the time-harmonic elastic wave equation at multiple frequencies ⋮ An inversion algorithm for a banded matrix ⋮ Direct approach to the band completion problem ⋮ Tridiagonal M-matrices whose inverse is tridiagonal and related pentadiagonal matrices ⋮ A novel algorithm for inverting a general \(k\)-tridiagonal matrix

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