[1] El-Mikkawy, M.E.A. (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
[2] El-Mikkawy, M.E.A. and Karawia, A. (2006) Inversion of General Tridiagonal Matrices. Applied Mathematics Letters, 19, 712-720. http://dx.doi.org/10.1016/j.aml.2005.11.012
[3] Akin, H. (2012) On 1D Reversible Cellular Automata with Reflective Boundary over the Prime Field of Order p. International Journal of Modern Physics C, 23, 1-13.
http://dx.doi.org/10.1142/s0129183111017020
[4] Chant, T.F. and Resascot, D.C. (1986) Generalized Deflated Block-Elimination. SIAM Journal on Numerical Analysis, 23, 913-924. http://dx.doi.org/10.1137/0723059
[5] El-Mikkawy, M.E.A. (1991) An Algorithm for Solving Tridiagonal Systems. Journal of Institute of Mathematics and Computer Sciences. Computer Sciences Series, 4, 205-210.
[6] El-Mikkawy, M.E.A. (2003) A Note on a Three-Term Recurrence for a Tridiagonal Matrix. Applied Mathematics and Computation, 139, 503-511. http://dx.doi.org/10.1016/S0096-3003(02)00212-6
[7] El-Mikkawy, M.E.A. (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
[8] El-Mikkawy, M.E.A. (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
[9] El-Mikkawy, M.E.A. and Rahmo, E.-D. (2008) A New Recursive Algorithm for Inverting General Tridiagonal and Anti-Tridiagonal Matrices. Applied Mathematics and Computation, 204, 368-372.
http://dx.doi.org/10.1016/j.amc.2008.06.053
[10] El-Mikkawy, M.E.A. and Rahmo, E.-D. (2009) A New Recursive Algorithm for Inverting General Periodic Pentadiagonal and Anti-Pentadiagonal Matrices. Applied Mathematics and Computation, 207, 164-170.
http://dx.doi.org/10.1016/j.amc.2008.10.010
[11] El-Mikkawy, M.E.A. and Rahmo, E. (2010) Symbolic Algorithm for Inverting Cyclic Pentadiagonal Matrices Recursively—Derivation and Implementation. Computers & Mathematics with Applications, 59, 1386-1396. http://dx.doi.org/10.1016/j.camwa.2009.12.020
[12] El-Mikkawy, M.E.A. (2012) A Generalized Symbolic Thomas Algorithm. Applied Mathematics, 3, 342-345.
http://dx.doi.org/10.4236/am.2012.34052
[13] Kavcic, A. and Moura, J.M.F. (2000) Matrices with Banded Inverses: Inversion Algorithms and Factorization of Gauss-Markov Processes. IEEE Transactions on Information Theory, 46, 1495-1509.
http://dx.doi.org/10.1109/18.954748
[14] Li, H.B., Huang, T.Z., Liu X.P. and Li, H. (2010) On the Inverses of General Tridiagonal Matrices. Linear Algebra and Its Applications, 433, 965-983. http://dx.doi.org/10.1016/j.laa.2010.04.042
[15] Shapiro, L.W. (1984) Positive Definite Matrices and Catalan Numbers, Revisited. Proceedings of the American Mathematical Society, 90, 488-496. http://dx.doi.org/10.1090/S0002-9939-1984-0728375-5
[16] Sogabe, T. (2007) On a Two-Term Recurrence for the Determinant of a General Matrix. Applied Mathematics and Computation, 187, 785-788. http://dx.doi.org/10.1016/j.amc.2006.08.156
[17] Sugimoto, T. (2012) On an Inverse Formula of a Tridiagonal Matrix. Operators and Matrices, 6, 465-480.
http://dx.doi.org/10.7153/oam-06-30
[18] Usmani, R. (1994) Inversion of a Tridiagonal Jacobi Matrix. Linear Algebra and Its Applications, 212/213, 413-414. http://dx.doi.org/10.1016/0024-3795(94)90414-6
[19] Akbudak, K., Kayaaslan, E. and Aykanat, C. (2012) Analyzing and Enhancing OSKI for Sparse Matrix-Vector Multiplication. www.prace-ri.eu
[20] Amodio, P., Gladwelly, I. and Romanazzi, G. (2006) Numerical Solution of General Bordered ABD Linear Systems by Cyclic Reduction. Journal of Numerical Analysis, Industrial and Applied Mathematics, 1, 5-12.
[21] Doedel, E. (1991) Numerical Analysis and Control of Bifurcation Problems (I): Bifurcation in Finite Dimensions. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 1, 493-520. http://dx.doi.org/10.1142/S0218127491000397
[22] Duff, I.S. and Scott, J.A. (2004) Stabilized Bordered Block Diagonal Forms for Parallel Sparse Solvers, RAL-TR-2004-006. http://www.numerical.rl.ac.uk/reports/reports.html
[23] da Fonseca, C.M. (2006) A Note on the Inversion of Acyclic Matrices. International Journal of Pure and Applied Mathematics, 31, 307-317.
[24] Martin, A. and Boyd, I.D. (2010) Variant of the Thomas Algorithm for Opposite-Bordered Tridiagonal Systems of Equations. International Journal for Numerical Methods in Biomedical Engineering, 26, 752-759. http://dx.doi.org/10.1002/cnm.1172
[25] Pajic, S. (2007) Power System State Estimation and Contingency Constrained Optimal Power Flow a Numerically Robust Implementation. PhD Thesis, Worcester-Polytechnic Institute, Worcester.
[26] Rashidinia, J. and Jalilian, R. (2009) Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems. World Academy of Science, Engineering and Technology. International Scholarly and Scientific Research & Innovation, 3, 167-173.
[27] Udala, A., Reedera, R., Velmrea, E. and Harrisonb, P. (2006) Comparison of Methods for Solving the Schrodinger Equation for Multiquantum Well Heterostructure Applications. Proceedings of the Estonian Academy of Sciences, Engineering, 12, 246-261.
[28] Wang, X.B. (2009) A New Algorithm with Its Scilab Implementation for Solution of Bordered Tridiagonal Linear Equations. 2009 IEEE International Workshop on Open-Source Software for Scientific Computation (OSSC), Guiyang, 18-20 September 2009, 11-14.
[29] Golub, G. and Van Loan, C. (1996) Matrix Computations. Third Edition, The Johns Hopkins University Press, Baltimore and London.
[30] El-Mikkawy, M.E.A. and Atlan, F. (2014) Algorithms for Solving Doubly Bordered Tridiagonal Linear Systems. British Journal of Mathematics & Computer Science, 4, 1246-1267.
http://dx.doi.org/10.9734/BJMCS/2014/8835
[31] Burden, R.L. and Faires, J.D. (2001) Numerical Analysis. Seventh Edition, Books & Cole Publishing, Pacific Grove.
[32] Karawia, A.A. (2013) Symbolic Algorithm for Solving Comrade Linear Systems Based on a Modified Stair-Diagonal Approach. Applied Mathematics Letters, 26, 913-918.
http://dx.doi.org/10.1016/j.aml.2012.10.019
[33] Karawia, A.A. (2012) A New Recursive Algorithm for Inverting a General Comrade Matrix. CoRR abs/1210.4662.
[34] Karawia, A.A. and Rizvi, Q.M. (2013) On Solving a General Bordered Tridiagonal Linear System. International Journal of Mathematics and Mathematical Sciences, 33, 1160-1163.