Research on Toeplitz Pentadiagonal linear system
Date Issued
2006
Date
2006
Author(s)
Tai, Tien-Chi
DOI
en-US
Abstract
When we solve some problems on computer calculation, we can convert
the series of computing to the banded linear system. Then the key of
the computing speed is the computing of matrix linear system. Along
with the problems, the banded matrix may be tridiagonal or
pentadiagonal or more. We try to improve the computing speed of the
matrix linear system to obtain better efficiency of solving the
problem.
Because the works of tridiagonal linear system were well
enough, we take the focus on pentadiagonal linear system.
Then we surveyed some recent topics about pentadiagonal matrix.
With these survey, we can get more understandings about the
pentadiagonal linear system.
In this thesis, We show what pentadiagonal matrix is and
pentadiagonal system of linear equation First.
In order to show the practicality of the pentadiagonal
system, we choose an example using pentadiagonal
system of linear equation to solve the problem.
Second, we select two methods that could solve the special kind of
pentadiagonal linear equation system, and introduce these methods to
see the merits and demerits of them.
Finally we focus on the performance of solving pentadiagonal
Toeplitz matrix. In this work, we propose the new approach for
solving real symmetric pentadiagonal Toeplitz matrix systems of
linear equations. Our algorithm entails fewer floating-point
operations when it be compared with Gaussian elimination method.
According to our experiment result, our result can be solve the
shallow water problem faster than Gaussian elimination.
Subjects
五對角線
矩陣系統
pentadiagonal
linear system
Type
thesis