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A Generalized Symbolic Thomas Algorithm

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DOI: 10.4236/am.2012.34052    4,573 Downloads   8,840 Views   Citations

ABSTRACT

The current paper is mainly devoted to construct a generalized symbolic Thomas algorithm that will never fail. Two new efficient and reliable computational algorithms are given. The algorithms are suited for implementation using computer algebra systems (CAS) such as Mathematica, Macsyma and Maple. Some illustrative examples are given.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. El-Mikkawy, "A Generalized Symbolic Thomas Algorithm," Applied Mathematics, Vol. 3 No. 4, 2012, pp. 342-345. doi: 10.4236/am.2012.34052.

References

[1] M. E. A. El-Mikkawy, “A Note on a Three-Term Recurrence for a Tridiagonal Matrix,” Applied Mathematics and Computation, Vol. 139, No. 2-3, 2003, pp. 503-511. doi:10.1016/S0096-3003(02)00212-6
[2] M. E. A. El-Mikkawy, “On the Inverse of a General Tridiagonal Matrix,” Applied Mathematics and Computation, Vol. 150, No. 3, 2004, pp. 669-679. doi:10.1016/S0096-3003(03)00298-4
[3] M. E. A. El-Mikkawy and A. Karawia, “Inversion of General Tridiagonal Matrices,” Applied Mathematics Letters, Vol. 19, No. 8, 2006, pp. 712-720. doi:10.1016/j.aml.2005.11.012
[4] M. El-Mikkawy and T. Sogabe, “A New Family of k-Fibonacci Numbers,” Applied Mathematics and Computation, Vol. 215, No. 12, 2010, pp. 4456-4461. doi:10.1016/j.amc.2009.12.069
[5] T. Sogabe and M. El-Mikkawy, “Fast Block Diagonalization of k-Tridiagonal Matrices,” Applied Mathematics and Computation, Vol. 218, No. 6, 2011, pp. 2740-2743. doi:10.1016/j.amc.2011.08.014
[6] M. E. A. El-Mikkawy, “A Fast Algorithm for Evaluating nth Order Tridiagonal Determinants,” Journal of Computational and Applied Mathematics, Vol. 166, No. 2, 2004, pp. 581-584. doi:10.1016/j.cam.2003.08.044
[7] R. L. Burden and J. D. Faires, “Numerical Analysis,” 7th Edition, Books & Cole Publishing, Pacific Grove, 2001.
[8] A. Yalciner, “The LU Factorization and Determinants of the k-Tridiagonal Matrices,” Asian-European Journal of Mathematics, Vol. 4, No. 1, 2011, pp. 187-197. doi:10.1142/S1793557111000162

  
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