A fast algorithm for solving banded Toeplitz systems

Belhaj, Skander; Dridi, Marwa; Salam, A.

doi:10.1016/j.camwa.2015.10.010

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Inverse Of a Banded Toeplitz Matrix2

Introduction1

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Cited by 3 publications

(3 citation statements)

References 12 publications

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“…The approach consists in embedding the banded Toeplitz matrix in a larger triangular Toeplitz matrix [12].…”

Section: Inverse Of a Banded Toeplitz Matrixmentioning

confidence: 99%

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A new algorithm for solving Toeplitz linear systems

Aoulad,

Tajani

2023

Math. Model. Comput.

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In this paper, we are interested in solving the Toeplitz linear systems. By exploiting the special Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman–Morrison formula, we propose an efficient algorithm for solving the considered problem. A typical example is presented to illustrate the different steps of the proposed algorithm. In addition, numerical tests are given showing the efficiency of our algorithm.

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“…The approach consists in embedding the banded Toeplitz matrix in a larger triangular Toeplitz matrix [12].…”

Section: Inverse Of a Banded Toeplitz Matrixmentioning

confidence: 99%

“…Theorem 1 (Ref. [12]). Let T b be a nonsingular banded Toeplitz matrix and M its associated lower triangular matrix.…”

Section: Inverse Of a Banded Toeplitz Matrixmentioning

confidence: 99%

A new algorithm for solving Toeplitz linear systems

Aoulad,

Tajani

2023

Math. Model. Comput.

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“…A very extensive study for the problem of solving linear system with banded Toeplitz structure can be founded in [10]. In the scalar case, this problem was studied recently via the technique of embedding the matrix T as a triangular Toeplitz matrix [2] and by using a fast inversion of a triangular Toeplitz matrix [1].…”

Section: Introductionmentioning

confidence: 99%

A fast algorithm of two-level banded Toeplitz systems of linear equations with application to image restoration

Dridi¹,

Belhaj²

2017

ntmsci

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Abstract:A fast algorithm is proposed for the solution of nm × nm block banded Toeplitz systems with banded Toeplitz blocks (BBTBTB). The algorithm consists of using the idea of embedding a BBTBTB matrix in a m × (n + k) block-triangular Toeplitz matrix. The computational complexity of the proposed algorithm is O(m 2 nlogn + m 3 n + k 3 m 3 ). The validity of the approach is illustrated by an application to image restoration.

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A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems

Kamra

Rao

2021

Mathematics and Computers in Simulation

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A fast algorithm for solving banded Toeplitz systems

Cited by 3 publications

References 12 publications

A new algorithm for solving Toeplitz linear systems

A new algorithm for solving Toeplitz linear systems

A fast algorithm of two-level banded Toeplitz systems of linear equations with application to image restoration

A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems

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