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On a recurrence for permanents of a sequence of 3-tridiagonal matrices

Trojovský Pavel, Zvoníková Iva

Journal of Applied Mathematics and Computational Mechanics

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2019

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Vol. 18, nr 4

95--100

EN

This is a corrigendum of the paper: Küçük, A. Z. & Düz, M. (2017). Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz and the Chebyshev polynomials. Journal of Applied Mathematics and Computational Mechanics, 16, 75-86. We will show that Remark 9, on page 84, does not hold, what is the consequence of the incorrect proof, which authors formulated there.

2

A numerical algorithm for computing the inverse of a Toeplitz pentadiagonal matrix

Talibi B., Hadj D. A., Sarsri D.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

83--95

EN

In the current paper, we present a computationally efficient algorithm for obtaining the inverse of a pentadiogonal toeplitz matrix. Few conditions are required, and the algorithm is suited for implementation using computer algebra systems.

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Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz matrix and the Chebyshev polynomials

Kucuk A. Z., Duz M.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 1

75--86

EN

In this study, the recursive relations between the permanents of a certain type of the k-tridiagonal symmetric Toeplitz matrix with complex entries and the Chebyshev polynomials of the second kind are presented.

4

Eigenvalues of 2-tridiagonal Toeplitz matrix

Borowska J., Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 4

11--17

EN

In this article an explicit formula for eigenvalues of a 2-tridiagonal Toeplitz matrix can be derived on the basis of a certain relation between the determinant of this matrix and the determinant of a pertinent tridiagonal matrix. It can be pointed out that the problem is investigated without imposing any conditions on the elements of matrix.

5

Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix

Borowska J., Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 4

19--26

EN

In this paper we show that the determinant of heptadiagonal symmetric Toeplitz matrix can be represented by a particular solution of the system of three homogeneous linear recurrence equations. The general considerations are illustrated by certain numerical example implementated in the Maple system.

6

Another Constructed Chaotic Image Encryption Scheme Based on Toeplitz Matrix and Hankel Matrix

Ye G.

Fundamenta Informaticae

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2010

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Vol. 101, nr 4

321-333

EN

This paper presents a novel image encryption scheme based on Toeplitz matrix and Hankel matrix. According to the definition and the expression of Toeplitz matrix and Hankel matrix, we permutate the positions of image pixels to confuse the relationship between the plain-image and cipher-image, and construct a new key. To enhance security further, hyper-chaos system of L¨u and Chen is taken to change the grey distribution of image pixels simultaneously. Numerical experimental results demonstrate that the key space is large enough, and the key is sensitive to initial conditions to resist the brute-force attack in the proposed scheme. Additionally, the distribution of grey values in encrypted image has a random-like behavior to resist statistical analysis. The proposed encryption scheme in this paper can suggest a high secure and efficient way for real-time image encryption and transmission in practice.