-
2
-
-
0000321992
-
Explicit solutions of linear matrix equation
-
Lancaster P. Explicit solutions of linear matrix equation. SIAM Review 1970; 12:544-566.
-
(1970)
SIAM Review
, vol.12
, pp. 544-566
-
-
Lancaster, P.1
-
3
-
-
43049173308
-
Dimension Reduction of Large-scale Systems
-
Benner P, Mehrmann V; Sorensen D eds, Springer: Berlin, Heidelberg, Germany
-
Benner P, Mehrmann V; Sorensen D (eds). Dimension Reduction of Large-scale Systems. Lecture Notes in Computational Science and Engineering, vol. 45. Springer: Berlin, Heidelberg, Germany, 2005.
-
(2005)
Lecture Notes in Computational Science and Engineering
, vol.45
-
-
-
4
-
-
0019533482
-
Principal component analysis in linear systems: Controllability, observability, and model reduction
-
Moore B. Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Transactions on Automatic Control 1981; AC-26:17-32.
-
(1981)
IEEE Transactions on Automatic Control
, vol.AC-26
, pp. 17-32
-
-
Moore, B.1
-
5
-
-
0020704532
-
On the structure of balanced and other principal representations of SISO systems
-
Fernando K, Nicholson H. On the structure of balanced and other principal representations of SISO systems. IEEE Transactions on Automatic Control 1983; 28(2):228-231.
-
(1983)
IEEE Transactions on Automatic Control
, vol.28
, Issue.2
, pp. 228-231
-
-
Fernando, K.1
Nicholson, H.2
-
6
-
-
84976855597
-
Solution of the matrix equation AX+XB=C: Algorithm 432
-
Bartels RH, Stewart GW. Solution of the matrix equation AX+XB=C: algorithm 432. Communications of the ACM 1972; 15:820-826.
-
(1972)
Communications of the ACM
, vol.15
, pp. 820-826
-
-
Bartels, R.H.1
Stewart, G.W.2
-
7
-
-
84976797154
-
Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations
-
Enright W. Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations. ACM Transactions on Mathematical Software 1978; 4:127-136.
-
(1978)
ACM Transactions on Mathematical Software
, vol.4
, pp. 127-136
-
-
Enright, W.1
-
12
-
-
38249030580
-
Iterative solution of the Lyapunov matrix equation
-
Wachspress E. Iterative solution of the Lyapunov matrix equation. Applied Mathematics Letters 1988; 107:87-90.
-
(1988)
Applied Mathematics Letters
, vol.107
, pp. 87-90
-
-
Wachspress, E.1
-
13
-
-
0019069037
-
Linear model reduction and solution of the algebraic Riccati equation by use of the sign function
-
CUED/B-Control, Engineering Department, Cambridge University
-
Roberts JD. Linear model reduction and solution of the algebraic Riccati equation by use of the sign function. International Journal of Control 1980; 32:677-687. Reprint of Technical Report No. TR-13, CUED/B-Control, Engineering Department, Cambridge University, 1971.
-
(1971)
International Journal of Control 1980; 32:677-687. Reprint of Technical Report No. TR-13
-
-
Roberts, J.D.1
-
15
-
-
0037103431
-
On the decay rate of Hankel singular values and related issues
-
Antoulas A, Sorensen D, Zhou Y. On the decay rate of Hankel singular values and related issues. Systems and Control Letters 2002; 46(5):323-342.
-
(2002)
Systems and Control Letters
, vol.46
, Issue.5
, pp. 323-342
-
-
Antoulas, A.1
Sorensen, D.2
Zhou, Y.3
-
16
-
-
10044281868
-
Existence of a low rank or H-matrix approximant to the solution of a Sylvester equation
-
Grasedyck L. Existence of a low rank or H-matrix approximant to the solution of a Sylvester equation. Numerical Linear Algebra with Applications 2004; 11:371-389.
-
(2004)
Numerical Linear Algebra with Applications
, vol.11
, pp. 371-389
-
-
Grasedyck, L.1
-
17
-
-
0033295674
-
A cyclic low rank Smith method for large sparse Lyapunov equations
-
Penzl T. A cyclic low rank Smith method for large sparse Lyapunov equations. SIAM Journal on Scientific Computing 2000; 21(4):1401-1418.
-
(2000)
SIAM Journal on Scientific Computing
, vol.21
, Issue.4
, pp. 1401-1418
-
-
Penzl, T.1
-
18
-
-
0003568779
-
-
Dissertation, University of Kiel, Kiel, Germany, in German, Available from
-
Grasedyck L. Theorie und Anwendungen Hierarchischer Matrizen. Dissertation, University of Kiel, Kiel, Germany, 2001 (in German). Available from: http://e-diss.uni-kiel.de/diss_454.
-
(2001)
Theorie und Anwendungen Hierarchischer Matrizen
-
-
Grasedyck, L.1
-
19
-
-
0141829814
-
Construction and arithmetics of ℋ-matrices
-
Grasedyck L, Hackbusch W. Construction and arithmetics of ℋ-matrices. Computing 2003; 70(4):295-334.
-
(2003)
Computing
, vol.70
, Issue.4
, pp. 295-334
-
-
Grasedyck, L.1
Hackbusch, W.2
-
20
-
-
0032637646
-
A sparse matrix arithmetic based on .ℋ-matrices. I. Introduction to ℋ-matrices
-
Hackbusch W. A sparse matrix arithmetic based on .ℋ-matrices. I. Introduction to ℋ-matrices. Computing 1999; 62(2):89-108.
-
(1999)
Computing
, vol.62
, Issue.2
, pp. 89-108
-
-
Hackbusch, W.1
-
21
-
-
0002133258
-
A sparse ℋ-matrix arithmetic. II. Application to multi-dimensional problems
-
Hackbusch W, Khoromskij BN. A sparse ℋ-matrix arithmetic. II. Application to multi-dimensional problems. Computing 2000; 64(1):21-47.
-
(2000)
Computing
, vol.64
, Issue.1
, pp. 21-47
-
-
Hackbusch, W.1
Khoromskij, B.N.2
-
22
-
-
0041340908
-
Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices
-
Grasedyck L, Hackbusch W, Khoromskij BN. Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices. Computing 2003; 70:121-165.
-
(2003)
Computing
, vol.70
, pp. 121-165
-
-
Grasedyck, L.1
Hackbusch, W.2
Khoromskij, B.N.3
-
23
-
-
33751525432
-
Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic
-
Baur U, Benner P. Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic. Computing 2006; 78(3):211-234.
-
(2006)
Computing
, vol.78
, Issue.3
, pp. 211-234
-
-
Baur, U.1
Benner, P.2
-
24
-
-
0033412866
-
Solving stable generalized Lyapunov equations with the matrix sign function
-
Benner P, Quintana-Ortí E. Solving stable generalized Lyapunov equations with the matrix sign function. Numerical Algorithms 1999; 20(1):75-100.
-
(1999)
Numerical Algorithms
, vol.20
, Issue.1
, pp. 75-100
-
-
Benner, P.1
Quintana-Ortí, E.2
-
25
-
-
0001175581
-
Design of a parallel nonsymmetric eigenroutine toolbox, part i
-
Sincovec RF et al, eds, SIAM: Philadelphia, PA
-
Bai Z, Demmel J. Design of a parallel nonsymmetric eigenroutine toolbox, part i. In Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, Sincovec RF et al. (eds). SIAM: Philadelphia, PA, 1993; 391-398.
-
(1993)
Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing
, pp. 391-398
-
-
Bai, Z.1
Demmel, J.2
-
26
-
-
55749088133
-
-
See also Technical Report CSD-92-718, Computer Science Division, University of California, Berkeley, CA.
-
See also Technical Report CSD-92-718, Computer Science Division, University of California, Berkeley, CA.
-
-
-
-
27
-
-
38249038136
-
Solving the algebraic Riccati equation with the matrix sign function
-
Byers R. Solving the algebraic Riccati equation with the matrix sign function. Linear Algebra and its Applications 1987; 85:267-279.
-
(1987)
Linear Algebra and its Applications
, vol.85
, pp. 267-279
-
-
Byers, R.1
-
30
-
-
0003706460
-
-
3rd edn, SIAM: Philadelphia, PA
-
Anderson E, Bai Z, Bischof C, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Sorensen D. LAPACK Users' Guide (3rd edn). SIAM: Philadelphia, PA, 1999.
-
(1999)
LAPACK Users' Guide
-
-
Anderson, E.1
Bai, Z.2
Bischof, C.3
Demmel, J.4
Dongarra, J.5
Du Croz, J.6
Greenbaum, A.7
Hammarling, S.8
McKenney, A.9
Sorensen, D.10
-
32
-
-
0032083879
-
Algorithm 782: Codes for rank-revealing QR factorizations of dense matrices
-
Bischof C, Quintana-Ortí G. Algorithm 782: codes for rank-revealing QR factorizations of dense matrices. ACM Transactions on Mathematical Software 1998; 24(2):254-257.
-
(1998)
ACM Transactions on Mathematical Software
, vol.24
, Issue.2
, pp. 254-257
-
-
Bischof, C.1
Quintana-Ortí, G.2
-
35
-
-
55749087935
-
Model reduction based on spectral projection methods
-
Dimension Reduction of Large-scale Systems, Benner P, Mehrmann V, Sorensen D eds, Springer: Berlin, Heidelberg, Germany
-
Benner P, Quintana-Ortí E. Model reduction based on spectral projection methods. In Dimension Reduction of Large-scale Systems, Benner P, Mehrmann V, Sorensen D (eds). Lecture Notes in Computational Science and Engineering, vol. 45. Springer: Berlin, Heidelberg, Germany, 2005; 5-45.
-
(2005)
Lecture Notes in Computational Science and Engineering
, vol.45
, pp. 5-45
-
-
Benner, P.1
Quintana-Ortí, E.2
|