New Algorithms And Properties For Some Special Matrices

This paper presents new algorithms for solving linear equations and inverse concerning block tridiagonal matrix , block pentadiagonal matrix and block period tridiagonal matrix. The study of these matrices has been an active field of research. The first reason for this circumstance is the fact that such matrices occur in a large variety of areas in computational mathematics and mathematical statistics etc. The second reason is that they have a lot of significant characteristic properties. Also, new properties of general Pascal matrices are given.The organization of the paper is as follows.In chapter 1, delineations and application of some special matrices are described and the well known Thomas algorithms are introduced.In chapter 2, variable parameter Thomas algorithms of solving linear systems, which coefficient matrices are block tridiagonal matrix and block pentadiagonal matrix, are given . Further we compare the new algorithms with Thomas algorithms by numerical examples.In chapter 3, according to the related results of the band matrix, we derive the new algorithms for inverting block tridiagonal matrices , block pentadiagonal matrices and block period tridiagonal matrix. At the same time we give numerical examples.In chapter 4, new algorithms for inverting block tridiagonal matrices , block pentadiagonal matrices and block period tridiagonal matrices are derived according to the recurrence methods. Last we give numerical examples.In chapter 5, new properties of general Pascal matrices are obtained.