An ℋ2 error expression for the Lanczos procedure

Proceedings of the IEEE Conference on Decision and Control

Volumn 2, Issue , 2003, Pages 1869-1872

  Gugercin, Serkan ^a   Antoulas, Athanasios C ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b Rice University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; EIGENVALUES AND EIGENFUNCTIONS; ERROR COMPENSATION; INTERPOLATION; ITERATIVE METHODS; MARKOV PROCESSES; SET THEORY; TRANSFER FUNCTIONS;

DYNAMICAL SYSTEMS; KRYLOV METHODS;

LARGE SCALE SYSTEMS;

EID: 1542320273     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. A.C. Antoulas, "On recursiveness and related topics in linear systems," IEEE Transactions on Automatic Control, AC-31, pp. 1121-1135 (1986).
2. A.C. Antoulas and J.C. Willems, "A behavioral approach to linear exact modeling," IEEE Transactions on Automatic Control, AC-38: 1776-1802 (1993).
3. A.C. Antoulas, "Recursive modeling of discrete-time time series," in IMA volume on Linear Algebra for Control, P. van Dooren and B.W. Wyman Editors, Springer Verlag, vol. 62: 1-20 (1993).
4. A.C. Antoulas and D.C. Sorensen, The Sylvester equation and approximate balanced reduction, Technical Report, November 2001.
5. W.E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quarterly of Applied Mathematics 9, pp: 17-29, 1951.
6. E.J. Grimme, D.C. Sorensen, and P. Van Dooren, Model reduction of state space systems via an implicitly restarted Lanczos method, Numerical Algorithms, 12: 1-31 (1995).
7. E.J. Grimme,Krylov Projection Methods for Model Reduction, Ph.D. Thesis, ECE Dept., U. of Illinois, Urbana-Champaign,(1997).
8. C. Lanczos, An iteration method for the solution of the eigenvalue problem for linear differential and integral operators, J. Res. Nat. Bur. Standards, 45, pp. 255-282, 1950.
9. A. Ruhe, Rational Krylov algorithms for nonsymmetric eigenvalue problems II: matrix pairs, Linear Alg. Appl., 197:283-295, (1984).
10. K. Gallivan, P. Van Dooren, and E. Grimme, A rational Lanczos algorithm for model reduction, Numerical Algorithms, 2(1-2):33-63, April 1996.
11. K. Gallivan, P. Van Dooren, and E. Grimme, On some recent developments in projection-based model reduction, in ENU-MATH 97 (Heidelberg), World Sci. Publishing, River Edge, NJ, 1998, pp. 98-113, 1998.
12. P. Van Dooren, The Lanczos algorithm and Padé approximations, Short Course, Benelux Meeting on Systems and Control, (1995).
13. th IFAC World Congress on Automatic Control, July 2002.
14. K. Gallivan, E. Grimme and P. Van Dooren, Model reduction of large-scale systems, rational Krylov versus balancing techniques, in Error control and adaptivity in scientific computing, pp: 177-190, Kluwer Acad. Publ., Dordrecht, 1999.
15. C. De Villemagne and R. Skelton, Model reduction using a projection formulation, International Jour. of Control, Vol 40, 2141-2169, 1987.
16. A. Varga, Balancing-free square-root algorithm for computing singular perturbation approximations, Proc. of 30th IEEE CDC, Brighton, UK, pp. 1062-1065, 1991.
17. A. Varga, On stochastic balancing related model reduction, Proc. of IEEE Conference on Decision and Control, CDC'2000, Sydney, Australia, 2000.
18. A. Yousouff, D. A. Wagie, and R. E. Skelton, Linar system approximation via covariance equivalent realizations, Journal of Math. Anal, and App., Vol. 196, 91-115, 1985.