Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices

Zheng, Yanpeng; Shon, Sugoog; Kim, Jangyoung

doi:10.1016/j.jmaa.2017.06.016

Cited by 15 publications

(4 citation statements)

References 36 publications

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“…Compared to an equivalent CPU implementation that utilizes a single CPU core, PSCR method indicated up to 24-fold speedups. Many studies have been conducted for tridiagonal matrices [13][14][15][16][17][18][19]. Typical results for their inverses include Usmani's algorithm [20] based on rudimentary matrix analysis, El-Mikkawy and Atlan's two symbolic algorithms [21,22] based on the Doolittle LU factorization of the k-tridiagonal matrix, Jia et al 's algorithms [23,24] based on block diagonalization technique, and so on.…”

Section: Introductionmentioning

confidence: 99%

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

Wei

Jiang

et al. 2019

Adv Differ Equ

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In this paper, we deal mainly with a class of periodic tridiagonal Toeplitz matrices with perturbed corners. By matrix decomposition with the Sherman–Morrison–Woodbury formula and constructing the corresponding displacement of matrices we derive the formulas on representation of the determinants and inverses of the periodic tridiagonal Toeplitz matrices with perturbed corners of type I in the form of products of Fermat numbers and some initial values. Furthermore, the properties of type II matrix can be also obtained, which benefits from the relation between type I and II matrices. Finally, we propose two algorithms for computing these properties and make some analysis about them to illustrate our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

Wei

Jiang

et al. 2019

Adv Differ Equ

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“…On the other hand, many studies have been conducted for tridiagonal matrices or periodic tridiagonal matrices, especially for their determinants and inverses [22][23][24][25][26][27][28][29][30]. Two decades ago, Wittenburg [31] studied the inverse of tridiagonal toeplitz and periodic matrices and applied them to elastostatics and vibration theory.…”

Section: Introductionmentioning

confidence: 99%

A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

et al. 2019

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In this paper, we study periodic tridiagonal Toeplitz matrices with perturbed corners. By using some matrix transformations, the Schur complement and matrix decompositions techniques, as well as the Sherman-Morrison-Woodbury formula, we derive explicit determinants and inverses of these matrices. One feature of these formulas is the connection with the famous Mersenne numbers. We also propose two algorithms to illustrate our formulas.

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“…Zheng et al [34] gave the decomposition formulas of a class of CUPL Toeplitz matrices. The explicit inverse of nonsingular conjugate-Toeplitz and conjugate-Hankel matrices are provided in [12,20].…”

Section: Introductionmentioning

confidence: 99%

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

Jiang¹,

Hong²,

Fu³

2017

J. Nonlinear Sci. Appl.

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In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are " similar" to the Toeplitz matrices. Their (−1, −1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (−1, 1)-circulants and (1, −1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.

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Cyclic displacements and decompositions of inverse matrices for CUPL Toeplitz matrices

Cited by 15 publications

References 36 publications

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

A Study of Determinants and Inverses for Periodic Tridiagonal Toeplitz Matrices with Perturbed Corners Involving Mersenne Numbers

Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix

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