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Closed-form expression for the inverse of a class of tridiagonal matrices
1. | Department of Petroleum and Applied Geophysics, Norwegian University of Science and Technology, Trondheim, Norway |
References:
[1] |
E. Asplund, Inverse of matrices {aij} which satisfy aj= 0 for j > i+p, Mathematica Scandinavia, 7 (1959), 57-60. |
[2] |
W. W. Barrett, A theorem on inverse of tridiagonal matrices, Linear Algebra and its Applications, 27 (1979), 211-217.
doi: 10.1016/0024-3795(79)90043-0. |
[3] |
J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
doi: 10.1137/1.9781611971446. |
[4] |
M. E. A. El-Mikkawy, On the inverse of a general tridiagonal matrix, Applied Mathematics and Computation, 150 (2004), 669-679.
doi: 10.1016/S0096-3003(03)00298-4. |
[5] |
D. K. Fadeev, Properties of a matrix, inverse to a hessenberg matrix, Journal of Sovjet Mathematics, 24 (1984), 118-120. |
[6] |
C. D. Fonseca, On the eigenvalues of some tridiagonal matrices, Journal of Computational and Applied Mathematics, 200 (2007), 283-286.
doi: 10.1016/j.cam.2005.08.047. |
[7] |
G. Hu and R. F. O'Connell, Analytical inversion of symmetric tridiagonal matrices, Journal of Physics A: Mathematical and General, 29 (1996), 1511-1513.
doi: 10.1088/0305-4470/29/7/020. |
[8] |
E. Kilic, Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions, Applied Mathematics and Computation, 197 (2008), 345-357.
doi: 10.1016/j.amc.2007.07.046. |
[9] |
R. K. Mallik, The inverse of a tridiagonal matrix, Linear Algebra and its Applications, 325 (2001), 109-139.
doi: 10.1016/S0024-3795(00)00262-7. |
[10] |
G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM Journal on Matrix Analysis and Applications, 13 (1992), 707-728.
doi: 10.1137/0613045. |
[11] |
K. S. Narendra and A. M. Annaswarny, Stable Adaptive Systems, Prentice Hall, 1989. |
[12] |
K. U. Siddiqui and M. K. Singh, Mechanical System Design, New Age International, 2007. |
[13] |
T. L. Smith and K. S. Smith, Mechanical Vibrations : Modeling and Measurement, Springer, 2011.
doi: 10.1007/978-1-4614-0460-6. |
[14] |
F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, Society of Industrial and Applied Mathematics, Review, 43 (2001), 235-286.
doi: 10.1137/S0036144500381988. |
[15] |
R. Usmani, Inversion of a tridiagonal jacobi matrix, Computers & Mathematics with Applications, 27 (1994), 59-66.
doi: 10.1016/0898-1221(94)90066-3. |
[16] |
R. Vandebril, M. V. Barel and N. Mastronardi, Matrix Computations and Semiseparable Matrices: Linear Systems, Johns Hopkins University Press, 2007. |
show all references
References:
[1] |
E. Asplund, Inverse of matrices {aij} which satisfy aj= 0 for j > i+p, Mathematica Scandinavia, 7 (1959), 57-60. |
[2] |
W. W. Barrett, A theorem on inverse of tridiagonal matrices, Linear Algebra and its Applications, 27 (1979), 211-217.
doi: 10.1016/0024-3795(79)90043-0. |
[3] |
J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997.
doi: 10.1137/1.9781611971446. |
[4] |
M. E. A. El-Mikkawy, On the inverse of a general tridiagonal matrix, Applied Mathematics and Computation, 150 (2004), 669-679.
doi: 10.1016/S0096-3003(03)00298-4. |
[5] |
D. K. Fadeev, Properties of a matrix, inverse to a hessenberg matrix, Journal of Sovjet Mathematics, 24 (1984), 118-120. |
[6] |
C. D. Fonseca, On the eigenvalues of some tridiagonal matrices, Journal of Computational and Applied Mathematics, 200 (2007), 283-286.
doi: 10.1016/j.cam.2005.08.047. |
[7] |
G. Hu and R. F. O'Connell, Analytical inversion of symmetric tridiagonal matrices, Journal of Physics A: Mathematical and General, 29 (1996), 1511-1513.
doi: 10.1088/0305-4470/29/7/020. |
[8] |
E. Kilic, Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions, Applied Mathematics and Computation, 197 (2008), 345-357.
doi: 10.1016/j.amc.2007.07.046. |
[9] |
R. K. Mallik, The inverse of a tridiagonal matrix, Linear Algebra and its Applications, 325 (2001), 109-139.
doi: 10.1016/S0024-3795(00)00262-7. |
[10] |
G. Meurant, A review on the inverse of symmetric tridiagonal and block tridiagonal matrices, SIAM Journal on Matrix Analysis and Applications, 13 (1992), 707-728.
doi: 10.1137/0613045. |
[11] |
K. S. Narendra and A. M. Annaswarny, Stable Adaptive Systems, Prentice Hall, 1989. |
[12] |
K. U. Siddiqui and M. K. Singh, Mechanical System Design, New Age International, 2007. |
[13] |
T. L. Smith and K. S. Smith, Mechanical Vibrations : Modeling and Measurement, Springer, 2011.
doi: 10.1007/978-1-4614-0460-6. |
[14] |
F. Tisseur and K. Meerbergen, The quadratic eigenvalue problem, Society of Industrial and Applied Mathematics, Review, 43 (2001), 235-286.
doi: 10.1137/S0036144500381988. |
[15] |
R. Usmani, Inversion of a tridiagonal jacobi matrix, Computers & Mathematics with Applications, 27 (1994), 59-66.
doi: 10.1016/0898-1221(94)90066-3. |
[16] |
R. Vandebril, M. V. Barel and N. Mastronardi, Matrix Computations and Semiseparable Matrices: Linear Systems, Johns Hopkins University Press, 2007. |
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