J. Appl. Math. Comput. Mech.

2013

DOI: 10.17512/jamcm.2013.3.03

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On determinant of certain pentadiagonal matrix

Jolanta Borowska¹,

Lena Łacińska²,

Jowita Rychlewska³

Abstract: Abstract. 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.

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Introduction3

The Modified Klein-gordon Model1

Eigenvalues Of a 2-tridiagonal Toeplitz Matrix1

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2014

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Cited by 11 publications

(10 citation statements)

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“…This paper constitutes generalization of results presented in [1]. Let us consider a pentadiagonal matrix of the form …”

Section: Introductionmentioning

confidence: 81%

Relation between determinants of tridiagonal and certain pentadiagonal matrices

¹

,

²

2014

J. Appl. Math. Comput. Mech.

Self Cite

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Abstract. 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.

“…This paper constitutes generalization of results presented in [1]. Let us consider a pentadiagonal matrix of the form …”

Section: Introductionmentioning

confidence: 81%

Relation between determinants of tridiagonal and certain pentadiagonal matrices

¹

,

²

2014

J. Appl. Math. Comput. Mech.

Self Cite

View full text Add to dashboard Cite

Abstract. 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.

“…, N in (1), i.e. D = 0, we obtain an ordered linear system, whose eigenvalue problem can be solved analytically [22][23][24][25] giving…”

Section: The Modified Klein-gordon Modelmentioning

confidence: 99%

Properties of Normal Modes in a Modified Disordered Klein-Gordon Lattice: From Disorder to Order

¹

,

²

,

³

et al. 2020

Nonlinear Phenomena in Complex Systems

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We introduce a modified version of the disordered Klein-Gordon lattice model, having two parameters for controlling the disorder strength: D, which determines the range of the coefficients of the on-site potentials, and W, which defines the strength of the nearestneighbor interactions. We fix W = 4 and investigate how the properties of the system's normal modes change as we approach its ordered version, i.e. D → 0. We show that the probability density distribution of the normal mode's frequencies takes a 'U'-shaped profile as D decreases. Furthermore, we use two quantities for estimating the mode's spatial extent, the so-called localization volume V (which is related to the mode's second moment) and the mode's participation number P. We show that both quantities scale as ∝ D−2 when D approaches zero and we numerically verify a proportionality relation between them as V/P ≈ 2.6.

“…It can be proved, [5], that Let us assume that matrix (24) has the even order n. In this case condition (26) has the form…”

Section: Eigenvalues Of a 2-tridiagonal Toeplitz Matrixmentioning

confidence: 99%

Eigenvalues of 2-tridiagonal Toeplitz matrix

¹

,

²

2015

J. Appl. Math. Comput. Mech.

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Abstract. 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.

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