On Solving Comrade Linear Systems Via Transformations
A. A. Karawia *
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt and Computer Science Unit, Deanship of Educational Services, Qassim University, P.O.Box 6595, Buraidah 51452, Saudi Arabia
S. S. Askar
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt and Department of Statistics and Operations Researches, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia
*Author to whom correspondence should be addressed.
Abstract
Recently, a new symbolic algorithm for solving comrade linear systems is given by Karawia [A. A. Karawia, Symbolic algorithm for solving comrade linear systems based on a modi fied Stair-Diagonal Approach, Appl. Math. Lett. 2013; 26:913-918.]. This paper introduces different numerical and symbolic algorithms for solving comrade linear systems via transformations. Our symbolic algorithm removes the cases where the numerical algorithms fail. The computational cost of these algorithms is given. It gives better absolute error than the other methods. The algorithm is implementable to the Computer Algebra System (CAS) such as MAPLE and MATLAB. Some illustrative examples are presented for the sake of illustration.
Keywords: Comrade matrices, tridiagonal matrices, determinants, Computer Algebra Systems (CAS)