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4 Journal of Applied Mathematics and Computational Mechanics

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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

2018

Vol. 17, nr 3

83--95

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.

Relation between determinants of tridiagonal and certain pentadiagonal matrices

Borowska J., Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 3

21--28

In this paper we consider a pentadiagonal matrix which consists of only three non-zero bands. We prove that the determinant of such a matrix can be represented by a product of two determinants of corresponding tridiagonal matrices. It is shown that such an approach gives greatly shorter time of computer calculations.

A system of linear recurrence equations for determinant of pentadiagonal matrix

Borowska J., Łacińska L., Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 2

5--12

In this paper we present an application of the system of two homogeneous linear recurrence equations to evaluate the determinant of pentadiagonal matrix. The general considerations are illustrated by two examples. It is shown that the proposed approach is suited for implementation using computer algebra systems.

On determinant of certain pentadiagonal matrix

Borowska J., Łacińska L., Rychlewska J.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 3

21--26

In this paper, using the LU factorization, the relation between the determinant of a certain pentadiagonal matrix and the determinant of a corresponding tridiagonal matrix will be derived. Moreover, it will be shown that determinant of this special pentadiagonal matrix can be calculated by applying the fourth order homogeneous linear difference equation.