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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.

Recurrent equations for the arithmetical and geometrical sequences of higher degree

Bryll A., Bryll G., Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2007

Vol. 12

155-162

Recurrent equations concern relationships between some (in general in a neighbourhood) elements of sequences. By these equations one can evaluate an arbitrary element of such sequences. In this paper we consider recurrent equations for the arithmetical and geometrical sequences of higher degree. We also give some properties of these sequences.