Abstract
In this paper, we develop a new algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems. Numerical experiments are given in order to illustrate the validity and efficiency of our algorithm.
Highlights
IntroductionWhere T is a quasi-pentadiagonal Toeplitz matrix. An n × n matrix T = (tij) is said to be Toeplitz if ti,j = ti−j
In this paper, we will focus on the problem of solving Tx = f (1)where T is a quasi-pentadiagonal Toeplitz matrix
We will take the pentadiagonal matrices which appear in the numerical solution of Kuramoto Sivashinsky (KS) equation as an example
Summary
Where T is a quasi-pentadiagonal Toeplitz matrix. An n × n matrix T = (tij) is said to be Toeplitz if ti,j = ti−j. Pentadiagonal matrices and quasi-pentadiagonal matrices frequently arise in many application areas, such as computational physics, scientific and engineering computings [3, 4, 5, 6], as well as in the wavefunction formalism [7] and density functional theory [8] in quantum chemistry The importance of these 15 applications motivated an extensive theoretical study of these kinds of matrices, such as determinant evaluation, eigenvalues computing and pentadiagonal linear systems solving in the last decades, see for example [9, 10] and a large literature therein. 25 we will introduce an algorithm for solving the diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems (1).
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