-
1
-
-
70449440430
-
Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation
-
Al-Mohy, A.H., Higham, N.J.: Computing the Fréchet derivative of the matrix exponential, with an application to condition number estimation. SIAM J. Matrix Anal. Appl. 30(4), 1639-1657 (2009)
-
(2009)
SIAM. J. Matrix Anal. Appl
, vol.30
, Issue.4
, pp. 1639-1657
-
-
Al-Mohy, A.H.1
Higham, N.J.2
-
2
-
-
77952552760
-
A New Scaling and Squaring Algorithm For the Matrix Exponential
-
The University of Manchester, UK. Revised April 2009, To appear in SIAM J. Matrix Anal. Appl
-
Al-Mohy, A.H., Higham, N.J.: A new scaling and squaring algorithm for the matrix exponential. MIMS EPrint 2009.9, Manchester Institute for Mathematical Sciences, The University of Manchester, UK. Revised April 2009 (2009) (To appear in SIAM J. Matrix Anal. Appl.)
-
(2009)
MIMS EPrint 2009.9, Manchester Institute For Mathematical Sciences
-
-
Al-Mohy, A.H.1
Higham, N.J.2
-
3
-
-
77952542410
-
-
Software Support for Metrology Best Practice Guide No. 11, National Physical Laboratory, Teddington
-
Cox, M.G., Harris, P.M.: Numerical analysis for algorithm design in metrology. Software Support for Metrology Best Practice Guide No. 11, National Physical Laboratory, Teddington (2004)
-
(2004)
Numerical Analysis For Algorithm Design In Metrology
-
-
Cox, M.G.1
Harris, P.M.2
-
4
-
-
1842865578
-
A Schur-Parlett algorithm for computing matrix functions
-
Davies, P.I., Higham, N.J.: A Schur-Parlett algorithm for computing matrix functions. SIAM J. Matrix Anal. Appl. 25(2), 464-485 (2003)
-
(2003)
SIAM J. Matrix Anal. Appl
, vol.25
, Issue.2
, pp. 464-485
-
-
Davies, P.I.1
Higham, N.J.2
-
5
-
-
0001345156
-
On condition numbers and the distance to the nearest ill-posed problem
-
Demmel, J.W.: On condition numbers and the distance to the nearest ill-posed problem. Numer. Math. 51, 251-289 (1987)
-
(1987)
Numer. Math
, vol.51
, pp. 251-289
-
-
Demmel, J.W.1
-
6
-
-
34547217286
-
A Schur-Newton method for the matrix pth root and its inverse
-
Guo, C.H., Higham, N.J.: A Schur-Newton method for the matrix pth root and its inverse. SIAM J. Matrix Anal. Appl. 28(3), 788-804 (2006)
-
(2006)
SIAM J. Matrix Anal. Appl
, vol.28
, Issue.3
, pp. 788-804
-
-
Guo, C.H.1
Higham, N.J.2
-
8
-
-
0025637437
-
Exploiting fast matrix multiplication within the level 3 BLAS
-
Higham, N.J.: Exploiting fast matrix multiplication within the level 3 BLAS. ACM Trans. Math. Softw. 16(4), 352-368 (1990)
-
(1990)
ACM Trans. Math. Softw
, vol.16
, Issue.4
, pp. 352-368
-
-
Higham, N.J.1
-
9
-
-
0012097416
-
Stability of a method for multiplying complex matrices with three real matrix multiplications
-
Higham, N.J.: Stability of a method for multiplying complex matrices with three real matrix multiplications. SIAM J. Matrix Anal. Appl. 13(3), 681-687 (1992)
-
(1992)
SIAM J. Matrix Anal. Appl
, vol.13
, Issue.3
, pp. 681-687
-
-
Higham, N.J.1
-
11
-
-
27144549311
-
The scaling and squaring method for the matrix exponential revisited
-
Higham, N.J.: The scaling and squaring method for the matrix exponential revisited. SIAM J. Matrix Anal. Appl. 26(4), 1179-1193 (2005)
-
(2005)
SIAM J. Matrix Anal. Appl
, vol.26
, Issue.4
, pp. 1179-1193
-
-
Higham, N.J.1
-
13
-
-
0034144755
-
A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra
-
Higham, N.J., Tisseur, F.: A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra. SIAM J. Matrix Anal. Appl. 21(4), 1185-1201 (2000)
-
(2000)
SIAM J. Matrix Anal. Appl
, vol.21
, Issue.4
, pp. 1185-1201
-
-
Higham, N.J.1
Tisseur, F.2
-
14
-
-
0032155271
-
GEMM-based level 3 BLAS: High performance model implementations and performance evaluation benchmark
-
Kågström, B., Ling, P., Van Loan, C.F.: GEMM-based level 3 BLAS: high performance model implementations and performance evaluation benchmark. ACM Trans. Math. Softw. 24(3), 268-302 (1998)
-
(1998)
ACM Trans. Math. Softw
, vol.24
, Issue.3
, pp. 268-302
-
-
Kågström, B.1
Ling, P.2
van Loan, C.F.3
-
16
-
-
34248588219
-
An error analysis of the modified scaling and squaring method
-
Koikari, S.: An error analysis of the modified scaling and squaring method. Comput. Math. Appl. 53, 1293-1305 (2007)
-
(2007)
Comput. Math. Appl
, vol.53
, pp. 1293-1305
-
-
Koikari, S.1
-
17
-
-
65849282797
-
Algorithm 894: On a block Schur-Parlett algorithm for φ{symbol}-functions based on the sep-inverse estimate
-
Article 12
-
Koikari, S.: Algorithm 894: On a block Schur-Parlett algorithm for φ{symbol}-functions based on the sep-inverse estimate. ACM Trans. Math. Software 36(2), Article 12 (2009)
-
(2009)
ACM Trans. Math. Software
, vol.36
, Issue.2
-
-
Koikari, S.1
-
18
-
-
45249107990
-
Extensions of the first and second complex-step derivative approximations
-
Lai, K.L., Crassidis, J.L.: Extensions of the first and second complex-step derivative approximations. J. Comput. Appl. Math. 219, 276-293 (2008)
-
(2008)
J. Comput. Appl. Math
, vol.219
, pp. 276-293
-
-
Lai, K.L.1
Crassidis, J.L.2
-
19
-
-
0038628504
-
Numerical algorithms based on the theory of complex variable
-
ACM, New York
-
Lyness, J.N.: Numerical algorithms based on the theory of complex variable. In: Proceedings of the 1967 22nd National Conference, pp. 125-133. ACM, New York (1967)
-
(1967)
Proceedings of The 1967 22nd National Conference
, pp. 125-133
-
-
Lyness, J.N.1
-
20
-
-
0000835942
-
Numerical differentiation of analytic functions
-
Lyness, J.N., Moler, C.B.: Numerical differentiation of analytic functions. SIAM J. Numer. Anal. 4(2), 202-210 (1967)
-
(1967)
SIAM J. Numer. Anal
, vol.4
, Issue.2
, pp. 202-210
-
-
Lyness, J.N.1
Moler, C.B.2
-
22
-
-
2442449533
-
The complex-step derivative approximation
-
Martins, J.R.R.A., Sturdza, P., Alonso, J.J.: The complex-step derivative approximation. ACM Trans. Math. Softw. 29(3), 245-262 (2003)
-
(2003)
ACM Trans. Math. Softw
, vol.29
, Issue.3
, pp. 245-262
-
-
Martins, J.R.R.A.1
Sturdza, P.2
Alonso, J.J.3
-
23
-
-
0001518003
-
Derivatives of the matrix exponential and their computation
-
Najfeld, I., Havel, T.F.: Derivatives of the matrix exponential and their computation. Adv. Appl. Math. 16, 321-375 (1995)
-
(1995)
Adv. Appl. Math
, vol.16
, pp. 321-375
-
-
Najfeld, I.1
Havel, T.F.2
-
24
-
-
34548210335
-
Accurate numerical derivatives in MATLAB
-
Article 26
-
Shampine, L.F.: Accurate numerical derivatives in MATLAB. ACM Trans. Math. Softw. 33(4), Article 26, 17 pages (2007)
-
(2007)
ACM Trans. Math. Softw
, vol.33
, Issue.4
, pp. 17
-
-
Shampine, L.F.1
-
25
-
-
58249092215
-
The scaling and modified squaring method for matrix functions related to the exponential
-
Skaflestad, B., Wright, W.M.: The scaling and modified squaring method for matrix functions related to the exponential. Appl. Numer. Math. 59, 783-799 (2009)
-
(2009)
Appl. Numer. Math
, vol.59
, pp. 783-799
-
-
Skaflestad, B.1
Wright, W.M.2
-
26
-
-
0032014469
-
Using complex variables to estimate derivatives of real functions
-
Squire, W., Trapp, G.: Using complex variables to estimate derivatives of real functions. SIAM Rev. 40(1), 110-112 (1998)
-
(1998)
SIAM Rev
, vol.40
, Issue.1
, pp. 110-112
-
-
Squire, W.1
Trapp, G.2
-
27
-
-
0031537607
-
Perturbation analysis of the matrix sign function
-
Sun, J.: Perturbation analysis of the matrix sign function. Linear Algebra Appl. 250, 177-206 (1997)
-
(1997)
Linear Algebra Appl
, vol.250
, pp. 177-206
-
-
Sun, J.1
|