The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows

Wei, Yunlan; Zheng, Yanpeng; Jiang, Zhaolin; Shon, Sugoog

doi:10.1007/s12190-021-01532-x

Cited by 12 publications

(4 citation statements)

References 23 publications

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“…Some applications of the new potential formula of the globe network are presented, such as some special and interesting potential formulae are given in Eqs. (33), (38), (41), (43), (46) and (48), respectively. The image numerical simulation using matlab has produced many interesting 3D dynamic views.…”

Section: Discussionmentioning

confidence: 99%

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Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Zhou

Zheng

Jiang

et al. 2022

Sci Rep

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Resistor network is widely used. Many potential formulae of resistor networks have been solved accurately, but the scale of data is limited by manual calculation, and numerical simulation has become the trend of large-scale operation. This paper improves the general solution of potential formula for an $$m\times n$$ m × n globe network. Chebyshev polynomials are introduced to represent new potential formula of a globe network. Compared with the original potential formula, it saves time to calculate the potential. In addition, an algorithm for computing potential by the famous second type of discrete cosine transform (DCT-II) is also proposed. It is the first time to be used for machine calculation. Moreover, it greatly increases the efficiency of computing potential. In the application of this new potential formula, the equivalent resistance formulae in special cases are given and displayed by three-dimensional dynamic view. The new potential formulae and the proposed fast algorithm realize large-scale operation for resistor networks.

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Section: Discussionmentioning

confidence: 99%

“…RT method needs eigenvalues of a tridiagonal matrix to represent the potential formula. At present, there have been many results on tridiagonal matrices [45][46][47][48][49][50][51] , which are also widely used. It can be said that it is a powerful tool to solve the resistor network [33][34][35][36][37][38][39][40][41][42][43] .…”

mentioning

confidence: 99%

Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Zhou

Zheng

Jiang

et al. 2022

Sci Rep

Self Cite

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“…Then they discussed the explosion of interest in them over the last two decades. Wei Y et al [24] presented explicit formulae for determinants, inverses and eigenpairs of a periodic tridiagonal Toeplitz-like matrix with asymmetrically perturbed rows. Solary et al [19] showed a symbolic algorithm for inverting a general k-heptadiagonal matrix and recursive relationships.…”

Section: Introductionmentioning

confidence: 99%

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

Thirupathi

Thamaraiselvan²

2023

Int. J. Anal. Appl.

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The k-tridiagonal matrices have received much attention in recent years. Many different algorithms have been proposed to improve the efficiency of k-tridiagonal matrix estimation. A novel method based on interval analysis has been identified to improve the efficiency of the calculation. This paper presents efficient and reliable computational algorithms for determining the determinant and inverse of general k-tridiagonal interval matrices built on generalized interval arithmetic. This study is based on the Doolittle LU factorization of the interval matrix. Finally, examples are presented to illustrate the algorithms.

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“…On the other hand, the importance of determinants, inverses, norms and spread in special matrix analysis, several authors [4,6,10,11,13,17,20,23,[28][29][30][31][32] have done some research on these special matrices. Recently, Jiang and Hong [12] studied the explicit form of determinants and inverses of Tribonacci r-circulant type matrices, while Zheng and Shon [36] gave the exact determinants and inverses of generalized Lucas skew circulant type matrices.…”

Section: Introductionmentioning

confidence: 99%

On determinants, inverses, norms, and spread of skew circulant matrices involving the product of Pell and Pell-Lucas numbers

Fan¹,

Wei²,

Zheng³

et al. 2023

J. Math. Computer Sci.

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In this paper, we discuss skew circulant matrices involving the product of Pell and Pell-Lucas numbers. The invertibility of the skew circulant matrices is investigated, while the fundamental theorems on the determinants and inverses of such matrices are derived by simple construction matrices. Specifically, the determinant and inverse of n × n skew circulant matrices can be expressed by the (n − 1)th, nth, (n + 1)th, (n + 2)th product of Pell and Pell-Lucas numbers. Some norms and bounds for spread of these matrices are given, respectively. In addition, we generalized these results to skew left circulant matrix involving the product of Pell and Pell-Lucas numbers. Finally, several numerical examples are illustrated to show the effectiveness of our theoretical results.

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The inverses and eigenpairs of tridiagonal Toeplitz matrices with perturbed rows

Cited by 12 publications

References 23 publications

Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Fast algorithm and new potential formula represented by Chebyshev polynomials for an $$m\times n$$ globe network

Symbolic Algorithm for Inverting General k-Tridiagonal Interval Matrices

On determinants, inverses, norms, and spread of skew circulant matrices involving the product of Pell and Pell-Lucas numbers

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