The Discriminance for FLDcircr Matrices and the Fast Algorithm of Their Inverse and Generalized Inverse
Affiliation(s)
College of Science, University of Shanghai for Science and Technology, Shanghai, China.
College of Science, University of Shanghai for Science and Technology, Shanghai, China.
ABSTRACT
This paper presents a new type of circulant matrices. We call it the first and the last difference r-circulant matrix (FLDcircr matrix). We can verify that the linear operation, the matrix product and the inverse matrix of this type of matrices are still FLDcircr matrices. By constructing the basic FLDcircr matrix, we give the discriminance for FLDcircr matrices and the fast algorithm of the inverse and generalized inverse of the FLDcircr matrices.
This paper presents a new type of circulant matrices. We call it the first and the last difference r-circulant matrix (FLDcircr matrix). We can verify that the linear operation, the matrix product and the inverse matrix of this type of matrices are still FLDcircr matrices. By constructing the basic FLDcircr matrix, we give the discriminance for FLDcircr matrices and the fast algorithm of the inverse and generalized inverse of the FLDcircr matrices.
Cite this paper
Pan, X. and Qin, M. (2015) The Discriminance for FLDcircr Matrices and the Fast Algorithm of Their Inverse and Generalized Inverse. Advances in Linear Algebra & Matrix Theory, 5, 54-61. doi: 10.4236/alamt.2015.52006.
Pan, X. and Qin, M. (2015) The Discriminance for FLDcircr Matrices and the Fast Algorithm of Their Inverse and Generalized Inverse. Advances in Linear Algebra & Matrix Theory, 5, 54-61. doi: 10.4236/alamt.2015.52006.
References
[1] Searle, S.R. (1979) On Inverting Circulant Matrices. Linear Algebra and Its Applications, 25, 77-89.
http://dx.doi.org/10.1016/0024-3795(79)90007-7 [2] Tolomei, P.B. and Torres, L.M. (2013) On the First Chvátal Closure of the Set Covering Polyhedron Related to Circulant Matrices. Electronic Notes in Discrete Mathematics, 44, 377-383.
http://dx.doi.org/10.1016/j.endm.2013.10.059 [3] Bozkurt, D. and Tam, T.-Y. (2012) Determinants and Inverses of Circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers. Applied Mathematics and Computation, 219, 544-551.
http://dx.doi.org/10.1016/j.amc.2012.06.039 [4] Wu, A.-G., Zeng, X.L., Duan, G.-R. and Wu, W.-J. (2010) Iterative Solutions to the Extended Sylvester-Conjugate Matrix Equations. Applied Mathematics and Computation, 217, 130-142.
http://dx.doi.org/10.1016/j.amc.2010.05.029 [5] Shen, S.Q. and Cen, J.M. (2010) On the Bounds for the Norms of r-Circulant Matrices with the Fibonacci and Lucas Numbers. Applied Mathematics and Computation, 216, 2891-2897.
http://dx.doi.org/10.1016/j.amc.2010.03.140 [6] Zellini, P. (1979) On Some Properties of Circulant Matrices. Linear Algebra and Its Applications, 26, 31-43.
http://dx.doi.org/10.1016/0024-3795(79)90170-8 [7] Davis, P.J. (1994) Circulant Matrices. 2nd Edition, Chelsea Publishing, New York. [8] Xu, Q.-Z., Li, H.-Q. and Jiang, Z.-L. (2005) An Algorithm for Finding the Minimal Polynomial of Fls r-Circulant Matrix. Journal of Mathematics (PRC), 25, 599-604. [9] He, C.Y. and Wang, X.Y. (2014) The Discriminance for a Special Class of Circulant Matrices and Their Diagonalization. Applied Mathematics and Computation, 238, 7-12.
http://dx.doi.org/10.1016/j.amc.2014.04.007 [10] Zhou, J.W. and Jiang, Z.L. (2014) The Spectral Norms of g-Circulant Matrices with Classical Fibonacci and Lucas Numbers Entries. Applied Mathematics and Computation, 233, 582-587.
http://dx.doi.org/10.1016/j.amc.2014.02.020 [11] Bell, C.L. (1981) Generalized Inverses of Circulant and Generalized Circulant Matrices. Linear Algebra and Its Applications, 39, 133-142.
http://dx.doi.org/10.1016/0024-3795(81)90297-4 [12] Jiang, Z.-J. and Xu, Z.-B. (2005) Efficient Algorithm for Finding the Inverse and the Group Inverse of FLSr-Circulant Matrix. Journal of Applied Mathematics and Computing, 18, 45-57.
http://dx.doi.org/10.1007/BF02936555
[1] Searle, S.R. (1979) On Inverting Circulant Matrices. Linear Algebra and Its Applications, 25, 77-89.
http://dx.doi.org/10.1016/0024-3795(79)90007-7 [2] Tolomei, P.B. and Torres, L.M. (2013) On the First Chvátal Closure of the Set Covering Polyhedron Related to Circulant Matrices. Electronic Notes in Discrete Mathematics, 44, 377-383.
http://dx.doi.org/10.1016/j.endm.2013.10.059 [3] Bozkurt, D. and Tam, T.-Y. (2012) Determinants and Inverses of Circulant Matrices with Jacobsthal and Jacobsthal-Lucas Numbers. Applied Mathematics and Computation, 219, 544-551.
http://dx.doi.org/10.1016/j.amc.2012.06.039 [4] Wu, A.-G., Zeng, X.L., Duan, G.-R. and Wu, W.-J. (2010) Iterative Solutions to the Extended Sylvester-Conjugate Matrix Equations. Applied Mathematics and Computation, 217, 130-142.
http://dx.doi.org/10.1016/j.amc.2010.05.029 [5] Shen, S.Q. and Cen, J.M. (2010) On the Bounds for the Norms of r-Circulant Matrices with the Fibonacci and Lucas Numbers. Applied Mathematics and Computation, 216, 2891-2897.
http://dx.doi.org/10.1016/j.amc.2010.03.140 [6] Zellini, P. (1979) On Some Properties of Circulant Matrices. Linear Algebra and Its Applications, 26, 31-43.
http://dx.doi.org/10.1016/0024-3795(79)90170-8 [7] Davis, P.J. (1994) Circulant Matrices. 2nd Edition, Chelsea Publishing, New York. [8] Xu, Q.-Z., Li, H.-Q. and Jiang, Z.-L. (2005) An Algorithm for Finding the Minimal Polynomial of Fls r-Circulant Matrix. Journal of Mathematics (PRC), 25, 599-604. [9] He, C.Y. and Wang, X.Y. (2014) The Discriminance for a Special Class of Circulant Matrices and Their Diagonalization. Applied Mathematics and Computation, 238, 7-12.
http://dx.doi.org/10.1016/j.amc.2014.04.007 [10] Zhou, J.W. and Jiang, Z.L. (2014) The Spectral Norms of g-Circulant Matrices with Classical Fibonacci and Lucas Numbers Entries. Applied Mathematics and Computation, 233, 582-587.
http://dx.doi.org/10.1016/j.amc.2014.02.020 [11] Bell, C.L. (1981) Generalized Inverses of Circulant and Generalized Circulant Matrices. Linear Algebra and Its Applications, 39, 133-142.
http://dx.doi.org/10.1016/0024-3795(81)90297-4 [12] Jiang, Z.-J. and Xu, Z.-B. (2005) Efficient Algorithm for Finding the Inverse and the Group Inverse of FLSr-Circulant Matrix. Journal of Applied Mathematics and Computing, 18, 45-57.
http://dx.doi.org/10.1007/BF02936555