An inversion algorithm for a banded matrix

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Abstract

In this paper, an inversion algorithm for a banded matrix is presented. The n twisted decompositions of a banded matrix are given first; then the inverse of the matrix is obtained, one column at time. The method is about two times faster than the standard method based on the LU decomposition, as is shown with the analysis of computing complexity and the numerical experiments.

Keywords

Banded matrix
Inverse
Twisted decomposition
The computing complexity
Tridiagonal matrix
Pentadiagonal matrix

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This research was supported by NSFC (10771030), the Key Project of Chinese Ministry of Education (107098), the Specialized Research Fund for the Doctoral Program of Higher Education (20070614001), Sichuan Province Project for Applied Basic Research (2008JY0052) and the Project of National Defense Key Lab. (9140C6902030906).