Recursive self preconditioning method based on Schur complement for Toeplitz matrices

Toutounian, Faezeh; Akhoundi, Nasser

doi:10.1007/s11075-012-9603-9

Numer Algor

2012

DOI: 10.1007/s11075-012-9603-9

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Recursive self preconditioning method based on Schur complement for Toeplitz matrices

Faezeh Toutounian

Nasser Akhoundi

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Cited by 3 publications

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Modify Levinson algorithm for symmetric positive definite Toeplitz system

Akhoundi

Alimirzaei

2015

Numer Algor

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This paper describes a new O(N 3 2 log(N)) solver for the symmetric positive definite Toeplitz system T N x N = b N . The method is based on the block QR decomposition of T N accompanied with Levinson algorithm and its generalized version for solving Schur complements S m of size m. In our algorithm we use a formula for displacement rank representation of the S m in terms of generating vectors of the matrix T N , and we assume that N = lm with l, m ∈ N. The new algorithm is faster than the classical O(N 2 )-algorithm for N > 2 9 . Numerical experiments confirm the good computational properties of the new method.

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Modify Levinson algorithm for symmetric positive definite Toeplitz system

Akhoundi

Alimirzaei

2015

Numer Algor

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Onk-step CSCS-based polynomial preconditioners for Toeplitz linear systems with application to fractional diffusion equations

Huang

et al. 2015

Applied Mathematics Letters

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A Suboptimal Fusion Estimation Algorithm Weighted by Matrices Based on LMI and Machine Learning

Wang

Hao

2023

IEEE Sensors J.

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Recursive self preconditioning method based on Schur complement for Toeplitz matrices

Cited by 3 publications

References 21 publications

Modify Levinson algorithm for symmetric positive definite Toeplitz system

Modify Levinson algorithm for symmetric positive definite Toeplitz system

Onk-step CSCS-based polynomial preconditioners for Toeplitz linear systems with application to fractional diffusion equations

A Suboptimal Fusion Estimation Algorithm Weighted by Matrices Based on LMI and Machine Learning

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