In the current article, the authors
present a new recurrence formula for the determinant of a banded matrix. An algorithm
for inverting general banded matrices is derived.
Cite this paper
Elouafi, M. and Ahmed, D. A. H. (2014). A New Algorithm for the Determinant and the Inverse of Banded Matrices. Open Access Library Journal, 1, e543. doi: http://dx.doi.org/10.4236/oalib.1100543.
Aiat Hadj, D. and Elouafi, M. (2008) A Fast Numerical Algorithm for the Inverse of a Tridiagonal and Pentadiagonal Matrix. Applied Mathematics and Computation, 202, 441-445. http://dx.doi.org/10.1016/j.amc.2008.02.026
Gravvanis, G.A. (2003) On the Solution of Boundary Value Problems by Using Fast Generalized Approximate Inverse Banded Matrix Techniques. The Journal of Supercomputing, 25, 119-129. http://dx.doi.org/10.1023/A:1023936410006
Ran, R.S. and Huang, T.Z. (2009) An Inversion Algorithm for a Banded Matrix. Computers and Mathematics with Applications, 58, 1699-1710. http://dx.doi.org/10.1016/j.camwa.2009.07.069
Trench, W.F. (1974) Inversion of Toeplitz Band Matrices. Mathematics of Computation, 28, 1089-1095. http://dx.doi.org/10.1090/S0025-5718-1974-0347066-8
Kratz, W. (2001) Banded Matrices and Difference Equa-tions. Linear Algebra and its Applications, 337, 1-20. http://dx.doi.org/10.1016/s0024-3795(01)00328-7
Aiat Hadj, A.D. and Elouafi, M. (2008) On the Characteristic Polynomial, Eigenvectors and Determinant of a Pentadiagonal Matrix. Applied Mathematics and Computation, 198, 634-642. http://dx.doi.org/10.1016/j.amc.2007.09.005