Theory and algorithm of the inversion method for pentadiagonal matrices
- 357 Downloads
A recently developed inversion method for pentadiagonal matrices is reconsidered in this work. The mathematical structure of the previously suggested method is fully developed. In the process of establishing the mathematical structure, certain determinantial relations specific to pentadiagonal matrices were also established. This led to a rather general necessary and sufficient condition for the method to work. All the so called forward and backward leading principal submatrices need to be non-singular. While this condition sounds restrictive it really is not so. These are in fact the conditions for forward and backward Gauss Eliminations without any pivoting requirement. Additionally, the method is more effective computational complexity wise then recently published competitive methods.
KeywordsDirect methods for linear systems and matrix inversion Difference equations Matrices, determinants
Unable to display preview. Download preview PDF.
- 2.Kanal M.E., Baykara N.A., Demiralp M.A.: A novel approach to the numerical inversion algorithm for adjacent pentadiagonal matrices. Tools Math. Model. 9, 270–280 (2003)Google Scholar
- 4.M.E. Kanal, Parallel algorithm on inversion for adjacent pentadiagonal matrices with MPI. J. Supercomput. (2010). doi: 10.1007/s11227-010-0487-y