-
1
-
-
0001874303
-
A multishift algorithm for the numerical solution of algebraic Riccati equations
-
G. Ammar, P. Benner, and V. Mehrmann, A multishift algorithm for the numerical solution of algebraic Riccati equations, Electron. Trans. Numer. Anal. 1:33-48 (1993).
-
(1993)
Electron. Trans. Numer. Anal.
, vol.1
, pp. 33-48
-
-
Ammar, G.1
Benner, P.2
Mehrmann, V.3
-
2
-
-
0021618667
-
Generalized eigenproblem algorithms and software for algebraic Riccati equations
-
W. Arnold, III, and A. Laub, Generalized eigenproblem algorithms and software for algebraic Riccati equations, Proc. IEEE 72:1746-1754 (1984).
-
(1984)
Proc. IEEE
, vol.72
, pp. 1746-1754
-
-
Arnold W. III1
Laub, A.2
-
3
-
-
33746924586
-
-
Tech. Rep. SPC 95_28, Fak f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG
-
P. Benner and H. Faβ bender, A Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem, Tech. Rep. SPC 95_28, Fak f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG, 1995.
-
(1995)
A Restarted Symplectic Lanczos Method for the Hamiltonian Eigenvalue Problem
-
-
Benner, P.1
Faß Bender, H.2
-
4
-
-
0003418313
-
-
Tech. Rep. SPC 95_22, Fak. f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG
-
P. Benner, A. Laub, and V. Mehrmann, A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equation I: Continuous-Time Case, Tech. Rep. SPC 95_22, Fak. f. Mathematik, TU Chemnitz-Zwickau, 09107 Chemnitz, FRG, 1995.
-
(1995)
A Collection of Benchmark Examples for the Numerical Solution of Algebraic Riccati Equation I: Continuous-Time Case
-
-
Benner, P.1
Laub, A.2
Mehrmann, V.3
-
5
-
-
38249035464
-
The weak and strong stability of algorithms in numerical algebra
-
J. Bunch, The weak and strong stability of algorithms in numerical algebra, Linear Algebra Appl. 88:49-66 (1987).
-
(1987)
Linear Algebra Appl.
, vol.88
, pp. 49-66
-
-
Bunch, J.1
-
7
-
-
0001423566
-
An analysis of the HR algorithm for computing the eigenvalues of a matrix
-
A. Bunse-Gerstner, An analysis of the HR algorithm for computing the eigenvalues of a matrix, Linear Algebra Appl. 35:155-173 (1981).
-
(1981)
Linear Algebra Appl.
, vol.35
, pp. 155-173
-
-
Bunse-Gerstner, A.1
-
8
-
-
38249039967
-
Matrix factorization for symplectic QR-like methods
-
A. Bunse-Gerstner, Matrix factorization for symplectic QR-like methods, Linear Algebra Appl. 83:49-77 (1986).
-
(1986)
Linear Algebra Appl.
, vol.83
, pp. 49-77
-
-
Bunse-Gerstner, A.1
-
9
-
-
0022914040
-
A symplectic QR-like algorithm for the solution of the real algebraic Riccati equation
-
A. Bunse-Gerstner and V. Mehrmann, A symplectic QR-like algorithm for the solution of the real algebraic Riccati equation, IEEE Trans. Automat. Control AC-31:1104-1113 (1986).
-
(1986)
IEEE Trans. Automat. Control
, vol.AC-31
, pp. 1104-1113
-
-
Bunse-Gerstner, A.1
Mehrmann, V.2
-
10
-
-
0003930438
-
-
Ph.D. Thesis, Dept. of Computer Science, Cornell Univ., Ithaca, N.Y.
-
R. Byers, Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation, Ph.D. Thesis, Dept. of Computer Science, Cornell Univ., Ithaca, N.Y., 1983.
-
(1983)
Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation
-
-
Byers, R.1
-
11
-
-
0001058962
-
A Hamiltonian QR-algorithm
-
_, A Hamiltonian QR-algorithm, SIAM J. Sci. Statist. Comput. 7:212-229 (1986).
-
(1986)
SIAM J. Sci. Statist. Comput.
, vol.7
, pp. 212-229
-
-
-
12
-
-
0001659028
-
A bisection method for measuring the distance of a stable to unstable matrices
-
_, A bisection method for measuring the distance of a stable to unstable matrices, SIAM J. Sci. Statist. Comput. 9:875-881 (1988).
-
(1988)
SIAM J. Sci. Statist. Comput.
, vol.9
, pp. 875-881
-
-
-
13
-
-
0002654780
-
An implicitly restarted Lanczos method for large symmetric eigenvalue problems
-
D. Calvetti, L. Reichet, and D. C. Sorensen, An implicitly restarted Lanczos method for large symmetric eigenvalue problems, Electron. Trans. Numer. Anal. 2:1-21 (1994).
-
(1994)
Electron. Trans. Numer. Anal.
, vol.2
, pp. 1-21
-
-
Calvetti, D.1
Reichet, L.2
Sorensen, D.C.3
-
14
-
-
0017012825
-
A decomposition of near-optimum regulators for systems with slow and fast modes
-
J. Chow and P. Kokotovic, A decomposition of near-optimum regulators for systems with slow and fast modes, IEEE Trans. Automat. Control AC-21:701-705 (1976).
-
(1976)
IEEE Trans. Automat. Control
, vol.AC-21
, pp. 701-705
-
-
Chow, J.1
Kokotovic, P.2
-
18
-
-
0000052549
-
On some algebraic problems in connection with general eigenvalue algorithms
-
L. Elsner, On some algebraic problems in connection with general eigenvalue algorithms, Linear Algebra Appl. 26:123-138 (1979).
-
(1979)
Linear Algebra Appl.
, vol.26
, pp. 123-138
-
-
Elsner, L.1
-
19
-
-
0041115364
-
-
Preprint 92-057, SFB 343, "Diskrete Strukturen in der Mathematik," Univ. Bielefeld, Bielefeld, FRG
-
U. Flaschka, Eine Variante des Lanczos-Algorithmus für große, dünn besetzte symmetrische Matrizen mit Blockstruktur, Preprint 92-057, SFB 343, "Diskrete Strukturen in der Mathematik," Univ. Bielefeld, Bielefeld, FRG, 1992.
-
(1992)
Eine Variante des Lanczos-Algorithmus für Große, Dünn Besetzte Symmetrische Matrizen mit Blockstruktur
-
-
Flaschka, U.1
-
20
-
-
0000394782
-
The QR transformation, Parts I and II
-
J. G. F. Francis, The QR transformation, Parts I and II, Comput. J. 4:265-271, 332-345 (1961).
-
(1961)
Comput. J.
, vol.4
, pp. 265-271
-
-
Francis, J.G.F.1
-
22
-
-
0041126767
-
Lanczos-type algorithms for structured non-Hermitian eigenvalue problems
-
(J. Brown, M. Chu, D. Ellison, and R. Plemmons, Eds.), SIAM
-
R. Freund, Lanczos-type algorithms for structured non-Hermitian eigenvalue problems, in Proceedings of the Cornelius Lanczos International Centenary Conference (J. Brown, M. Chu, D. Ellison, and R. Plemmons, Eds.), SIAM, 1994, pp. 243-245.
-
(1994)
Proceedings of the Cornelius Lanczos International Centenary Conference
, pp. 243-245
-
-
Freund, R.1
-
24
-
-
0001378925
-
An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices
-
R. W. Freund, M. H. Gutknecht, and N. M. Nachtigal, An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, SIAM J. Sci. Comput. 14:137-158 (1993).
-
(1993)
SIAM J. Sci. Comput.
, vol.14
, pp. 137-158
-
-
Freund, R.W.1
Gutknecht, M.H.2
Nachtigal, N.M.3
-
26
-
-
27544508073
-
Model reduction of state space systems via an implicitly restarted Lanczos method
-
E. Grimme, D. Sorensen, and P. Van Dooren, Model reduction of state space systems via an implicitly restarted Lanczos method, Numer. Algorithms 12:1-31 (1996).
-
(1996)
Numer. Algorithms
, vol.12
, pp. 1-31
-
-
Grimme, E.1
Sorensen, D.2
Van Dooren, P.3
-
27
-
-
0000497979
-
A completed theory of the unsymmetric Lanczos process and related algorithms, Part I
-
M. Gutknecht, A completed theory of the unsymmetric Lanczos process and related algorithms, Part I, SIAM J. Matrix Anal. Appl. 13:594-639 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 594-639
-
-
Gutknecht, M.1
-
28
-
-
0009165708
-
A completed theory of the unsymmetric Lanczos process and related algorithms, Part II
-
_, A completed theory of the unsymmetric Lanczos process and related algorithms, Part II, SIAM J. Matrix Anal. Appl. 15:15-58 (1994).
-
(1994)
SIAM J. Matrix Anal. Appl.
, vol.15
, pp. 15-58
-
-
-
29
-
-
0024178897
-
Heuristic approaches to the solution of very large sparse Lyapunov and algebraic Riccati equations
-
Austin, Tex.
-
A. Hodel and K. Poolla, Heuristic approaches to the solution of very large sparse Lyapunov and algebraic Riccati equations, in Proceedings of the 27th IEEE Conference on Decision and Control, Austin, Tex., 1988, pp. 2217-2222.
-
(1988)
Proceedings of the 27th IEEE Conference on Decision and Control
, pp. 2217-2222
-
-
Hodel, A.1
Poolla, K.2
-
31
-
-
0028377922
-
Krylov subspace methods for solving large Lyapunov equations
-
I. M. Jaimoukha and E. M. Kasenally, Krylov subspace methods for solving large Lyapunov equations, SIAM J. Numer. Anal. 31:227-251 (1994).
-
(1994)
SIAM J. Numer. Anal.
, vol.31
, pp. 227-251
-
-
Jaimoukha, I.M.1
Kasenally, E.M.2
-
32
-
-
0001390707
-
On some algorithms for the solution of the complete eigenvalue problem
-
V. N. Kublanoskaja, On some algorithms for the solution of the complete eigenvalue problem, U.S.S.R. Comput. Math. and Math. Phys. 3:637-657 (1961).
-
(1961)
U.S.S.R. Comput. Math. and Math. Phys.
, vol.3
, pp. 637-657
-
-
Kublanoskaja, V.N.1
-
34
-
-
0000094594
-
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
-
C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards 45:255-282 (1950).
-
(1950)
J. Res. Nat. Bur. Standards
, vol.45
, pp. 255-282
-
-
Lanczos, C.1
-
35
-
-
0002756084
-
Invariant subspace methods for the numerical solution of Riccati equations
-
(S. Bittanti, A. Laub, and J. Willems, Eds.), Springer-Verlag, Berlin
-
A. Laub, Invariant subspace methods for the numerical solution of Riccati equations, in The Riccati Equation (S. Bittanti, A. Laub, and J. Willems, Eds.), Springer-Verlag, Berlin, 1991, pp. 163-196.
-
(1991)
The Riccati Equation
, pp. 163-196
-
-
Laub, A.1
-
36
-
-
0007201647
-
-
Diplomarbeit, Univ. Bielefeld, Bielefeld, FRG
-
V. Mehrmann, Der SR-Algorithmus zur Berechnung der Eigenwerte einer Matrix, Diplomarbeit, Univ. Bielefeld, Bielefeld, FRG, 1979.
-
(1979)
Der SR-Algorithmus zur Berechnung der Eigenwerte Einer Matrix
-
-
Mehrmann, V.1
-
37
-
-
0003563831
-
-
Lecture Notes in Control and Inform. Sci. 163, Springer-Verlag, Heidelberg, July
-
_, The Autonomous Linear Quadratic Control Problem, Theory and Numerical Solution, Lecture Notes in Control and Inform. Sci. 163, Springer-Verlag, Heidelberg, July 1991.
-
(1991)
The Autonomous Linear Quadratic Control Problem, Theory and Numerical Solution
-
-
-
38
-
-
0041126766
-
-
Master's Thesis, Nanjing Aeronautical Inst., Campus P.O. Box 245, Nanjing, P.R. China
-
G. Mei, A New Method for Solving the Algebraic Riccati Equation, Master's Thesis, Nanjing Aeronautical Inst., Campus P.O. Box 245, Nanjing, P.R. China, 1986.
-
(1986)
A New Method for Solving the Algebraic Riccati Equation
-
-
Mei, G.1
-
39
-
-
33646526859
-
Solution of large matrix equations which occur in response theory
-
J. Olson, H. Jensen, and P. Jørgensen, Solution of large matrix equations which occur in response theory, J. Comput. Phys. 74:265-282 (1988).
-
(1988)
J. Comput. Phys.
, vol.74
, pp. 265-282
-
-
Olson, J.1
Jensen, H.2
Jørgensen, P.3
-
41
-
-
84966231631
-
A look-ahead Lanczos algorithm for unsymmetric matrices
-
B. N. Parlett, D. R. Taylor, and Z. A. Liu, A look-ahead Lanczos algorithm for unsymmetric matrices, Math. Comp. 44:105-124 (1985).
-
(1985)
Math. Comp.
, vol.44
, pp. 105-124
-
-
Parlett, B.N.1
Taylor, D.R.2
Liu, Z.A.3
-
42
-
-
0000010902
-
A multi-level technique for the approximate solution of operator Lyapunov and algebraic Riccati equations
-
I. Rosen and C. Wang, A multi-level technique for the approximate solution of operator Lyapunov and algebraic Riccati equations, SIAM J. Numer. Anal. 32:514-541 (1995).
-
(1995)
SIAM J. Numer. Anal.
, vol.32
, pp. 514-541
-
-
Rosen, I.1
Wang, C.2
-
43
-
-
0039347646
-
Algorithm GRICSR solving continuous-time algebraic Riccati equations using Gaussian symplectic transformations
-
V. Sima, Algorithm GRICSR solving continuous-time algebraic Riccati equations using Gaussian symplectic transformations, Stud. Res. Comp. Inf. 1:237-254 (1992).
-
(1992)
Stud. Res. Comp. Inf.
, vol.1
, pp. 237-254
-
-
Sima, V.1
-
44
-
-
0000322706
-
Implicit application of polynomial filters in a k-step Arnoldi method
-
D. C. Sorensen, Implicit application of polynomial filters in a k-step Arnoldi method, SIAM J. Matrix Anal. Appl. 13:357-385 (1992).
-
(1992)
SIAM J. Matrix Anal. Appl.
, vol.13
, pp. 357-385
-
-
Sorensen, D.C.1
-
45
-
-
0003820738
-
-
Ph.D. Thesis, Center for Pure and Applied Mathematics, Univ. of California, Berkeley
-
D. R. Taylor, Analysis of the Look-ahead Lanczos Algorithm, Ph.D. Thesis, Center for Pure and Applied Mathematics, Univ. of California, Berkeley, 1982.
-
(1982)
Analysis of the Look-ahead Lanczos Algorithm
-
-
Taylor, D.R.1
-
46
-
-
0000059741
-
A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
-
C. Van Loan, A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix, Linear Algebra Appl. 16:233-251 (1984).
-
(1984)
Linear Algebra Appl.
, vol.16
, pp. 233-251
-
-
Van Loan, C.1
|