In the current paper, the authors present a symbolic algorithm for solving doubly bordered k-tridiagonal linear system having n equations and n unknowns. The proposed algorithm is derived by using partition together with UL factorization. The cost of the algorithm is O(n). The algorithm is implemented using the computer algebra system, MAPLE. Some illustrative examples are given.
References
[1]
El-Mikkawy, M. (2003) A Note on a Three-Term Recurrencefor a Tridiagonal Matrix. Applied Mathematics and Computation, 139, 503-511. http://dx.doi.org/10.1016/S0096-3003(02)00212-6
[2]
El-Mikkawy, M. (2004) On the Inverse of a General Tridiagonal Matrix. Applied Mathematics and Computation, 150, 669-679. http://dx.doi.org/10.1016/S0096-3003(03)00298-4
[3]
El-Mikkawy, M. and Karawia, A. (2006) General Tridiagonal Matrices. Applied Mathematics Letters, 19, 712-720. http://dx.doi.org/10.1016/j.aml.2005.11.012
[4]
El-Mikkawy, M. and Rahmo, E. (2008) A New Recursive Algorithm for Inverting Tridiagonal and Anti-Tridiagonal Matrices. Applied Mathematics and Computation, 204, 368-372. http://dx.doi.org/10.1016/j.amc.2008.06.053
[5]
El-Mikkawy, M. and Sogabe, T. (2010) A New Family of k-Fibonacci Numbers. Applied Mathematics and Computation, 215, 4456-4461. http://dx.doi.org/10.1016/j.amc.2009.12.069
[6]
Jia, J., Sogabe, T. and El-Mikkawy, M. (2013) Inversion of k-Tridiagonal Matrices with Toeplitz Structure. Computers & Mathematics with Applications, 65, 116-125. http://dx.doi.org/10.1016/j.camwa.2012.11.001
[7]
El-Mikkawy, M. and Atlan, F. (2014) A Novel Algorithm for inverting a General k-Tridiagonal Matrix. Applied Mathematics Letters, 32, 41-47. http://dx.doi.org/10.1016/j.aml.2014.02.015
[8]
El-Mikkawy, M. (2012) A Generalized Symbolic Thomas Algorithm. Applied Mathematics, 3, 342-345. http://dx.doi.org/10.4236/am.2012.34052
[9]
El-Mikkawy, M. (2004) A Fast Algorithm for Evaluating nth Order Tri-Diagonal Determinants. Journal of Computational and Applied Mathematics, 166, 581-584. http://dx.doi.org/10.1016/j.cam.2003.08.044
[10]
El-Mikkawy, M. (2005) A New Computational Algorithm for Solving Periodic Tri-Diagonal Linear Systems. Applied Mathematics and Computation, 161, 691-696. http://dx.doi.org/10.1016/j.amc.2003.12.114
[11]
El-Mikkawy, M., El-Shehawy, M. and Shehab, N. (2015) Solving Doubly Bordered Tridiagonal Linear Systems via Partition. Applied Mathematics, 6, 967-978. http://dx.doi.org/10.4236/am.2015.66089
