A Completely Parallelizable Algorithm for the Determinant of a Tridiagonal Matrix

A. Mahmood, D. J. Lynch, L. D. Philipp


A new parallel algorithm (MIMD-PRAM class) having parallel time complexity of log2 n for computing the determinant of a tridiagonal matrix is developed. The algorithm is based on coupling the determinants of two neighboring submatrix blocks. With each coupling, the block size is increased by a factor of two until the entire determinant of an n x n matrix is found by the final coupling of two n/2 sized blocks. It is shown that the determinant of an n x n tridiagonal matrix can be computed in (3 log2 n - 2) parallel steps with a maximum parallel requirement of 7 ( n/4) + 3 processors. The algorithm achieves linear speedup as the number of processors is increased.


Determinant, Tridiagonal Matrix, Parallel Algorithm, MIMD, PRAM

Full Text:


Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

Crossref Similarity Check logo

Crossref logologo_doaj

 Hrvatski arhiv weba logo