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Application of second order inhomogeneous linear recurrences to solving a tridiagonal system

Borowska J., Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 2

5--10

In this paper we consider a linear system of algebraic equations of a tridiagonal type. We show that the solution of such a system can be represented by a corresponding second order inhomogeneous linear recurrence equation. This approach enables us to represent the solution to the tridiagonal Toeplitz linear system of equations in a closed form.

Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix

Borowska J., Łacińska L.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

19--26

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.

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.