[1]
|
L. Z. Lu and W. Sun, “The Minimal Eigenvalues of a Class of Block-Tridiagonal Matrices,” IEEE Transactions on Information Theory, Vol. 43, No. 2, 1997, pp. 787-791.
doi:10.1109/18.556141
|
[2]
|
C. F. Fischer and R. A. Usmani, “Properties of Some Tridiagonal Matrices and Their Application to Boundary Value Problems,” SIAM Journal on Numerical Analysis, Vol. 6, No. 1, 1969, pp. 127-142. doi:10.1137/0706014
|
[3]
|
G. D. Simth, “Numerical Solution of Partial Differential Equations: Finite Difference Methods,” 2nd Edition, Oxford University Press, New York, 1978.
|
[4]
|
R. M. M. Mattheij and M. D. Smooke, “Estimates for the Inverse of Tridiagonal Matrices Arising in Boundary-Value Problems,” Linear Algebra and Its Applications, Vol. 73, 1986, pp. 33-57. doi:10.1016/0024-3795(86)90232-6
|
[5]
|
P, Amodio and F. Mazzia, “A New Approach to the Backward Error Analysis in the LU Factorization Algorithm,” BIT Numerical Mathematics, Vol. 39, No. 3, 1999, pp. 385-402. doi:10.1023/A:1022358300517
|
[6]
|
E. Isaacson and H. B. Keller, “Analysis of Numerical Methods,” Wiley, New York, 1966.
|
[7]
|
R. E. Bank and D. J. Rose, “Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case,” SIAM Journal on Numerical Analysis, Vol. 14, No. 5, 1977, pp. 792-829. doi:10.1137/0714055
|
[8]
|
R. M. M. Mattheij, “The Stability of LU-Decompostions of Block Tridiagonal Matrices,” Bulletin of the Australian Mathematical Society, Vol. 29, No. 2, 1984, pp. 177-205.
doi:10.1017/S0004972700021432
|
[9]
|
P. Concus, G. H. Golub and G. Meurant, “Block Preconditioning for the Conjugate Method,” SIAM Journal on Scientific and Statistical Computing, Vol. 6, No. 1, 1985, pp. 220-252. doi:10.1137/0906018
|
[10]
|
J. M. Varah, “On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations,” Mathematics of Computation, Vol. 26, No. 120, 1972, pp. 859-868. doi:10.1090/S0025-5718-1972-0323087-4
|
[11]
|
R. E. Bank and D. J. Rose, “Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case,” SIAM Journal on Numerical Analysis, Vol. 14, No. 5, 1977, pp. 792-829. doi:10.1137/0714055
|
[12]
|
P. Yalamov and V. Pavlov, “Stability of the Block Cyclic Reduction,” Linear Algebra and Its Applications, Vol. 249, No. 1-3, 1996, pp. 341-358.
doi:10.1016/0024-3795(95)00392-4
|
[13]
|
J. W. Demmel and N. J. Higham, “Stability of Block Algorithms with Fast Level-3 BLAS,” ACM Transactions on Mathematical Software, Vol. 18, No. 3, 1992, pp. 274-291. doi:10.1145/131766.131769
|
[14]
|
J. W. Demmel, N. J. Higham and R. S. Schreiber, “Stability of Block LU Factorizaton, Numerical Linear Algebra with Applications,” Vol. 2, No. 2, 1995, pp. 173-190.
doi:10.1002/nla.1680020208
|
[15]
|
N. J. Higham, “Accuracy and Stability of Numerical Algorithm,” Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1996.
|