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(p,q)-Pentadiagonal matrices have received considerable attention in recent years, which are a generalization of pentadiagonal matrices. In this paper, a breakdown-free algorithm is presented for numerically evaluating the determinants of n-by-n (p,q)-pentadiagonal matrices. The algorithm is based on the use of a reliable tridiagonalization process which preserves the banded structure and sparsity of the original matrix. Numerical examples are given in order to illustrate the effectiveness of the proposed algorithm. All of the experiments are performed on a computer with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]

Hessenberg matrices frequently arise in many application areas and have been attracted much attention in recent years. In the current paper, we present two numerical algorithms of $$O(n^2)$$ for computing the determinant of an n-by- n general Hessenberg matrix. The algorithms are all suited for implementation using Computer Algebra Systems such as MATLAB and MAPLE. Some numerical examples are provided in order to demonstrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we present a fast numerical algorithm for solving nearly penta-diagonal linear systems and show that the computational cost is less than those of three algorithms in El-Mikkawy and Rahmo, [Symbolic algorithm for inverting cyclic penta-diagonal matrices recursively–Derivation and implementation, Comput. Math. Appl. 59 (2010), pp. 1386–1396], Lv and Le [A note on solving nearly penta-diagonal linear systems, Appl. Math. Comput. 204 (2008), pp. 707–712] and Neossi Nguetchue and Abelman [A computational algorithm for solving nearly penta-diagonal linear systems, Appl. Math. Comput. 203 (2008), pp. 629–634.]. In addition, an efficient way of evaluating the determinant of a nearly penta-diagonal matrix is also discussed. The algorithm is suited for implementation using computer algebra systems (CAS) such as MATLAB, MACSYMA and MAPLE. Some numerical examples are given in order to illustrate the efficiency of our algorithm. [ABSTRACT FROM AUTHOR]