Combinatorial relaxation algorithm for mixed polynomial matrices

Mathematical Programming, Series B

Volumn 90, Issue 2, 2001, Pages 353-371

  Iwata, Satoru ^a   Murota, Kazuo ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

Combinatorial relaxation; Index of DAE; Mixed matrix; Polynomial matrix; Valuated matroid

Indexed keywords

EID: 0942303541     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00011427     Document Type: Article

References (31)

1. Brenan, K.E., Campbell, S.L., Petzold, L.R. (1989): Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. North-Holland
2. Bujakiewicz, P. (1994): Maximum Weighted Matching for High Index Differential Algebraic Equations. Doctor Thesis, Delft University of Technology
3. Commault, C., Dion, J.-M., Perez, A. (1991): Disturbance rejection for structured systems. IEEE Trans. Automat. Control AC-36, 884-887
4. Dress, A.W.M., Terhalle, W. (1995): Well-layered maps and the maximum-degree k x k-subdeterminant of a matrix of rational functions. Appl. Math. Lett. 8, 19-23
5. Dress, A.W.M., Terhalle, W. (1995): Well-layered maps - A class of greedily optimizable set functions. Appl. Math. Lett. 8, 77-80
6. Dress, A.W.M., Wenzel, W. (1990): A new look at the greedy algorithm. Appl. Math. Lett. 3, 33-35
7. Dress, A.W.M., Wenzel, W. (1992): Valuated matroids. Adv. Math. 93, 214-250
8. Duff, I., Gear, C.W. (1986): Computing the structural index. SIAM J. Alg. Disc. Meth. 7, 594-603
9. Gear, C.W. (1988): Differential-algebraic equation index transformations. SIAM J. Sci. Stat. Comput. 9, 39-47
10. Gear, C.W. (1990): Differential algebraic equations, indices, and integral algebraic equations. SIAM J. Numer. Anal. 27, 1527-1534
11. Hairer, E., Wanner, G. (1991): Solving Ordinary Differential Equations II. Springer
12. Hovelaque, V., Commault, C., Dion, J.-M. (1996): Analysis of linear structured systems using primal-dual algorithm. Systems Control Lett. 27, 73-85
13. Iwata, S., Murota, K., Sakuta, I. (1996): Primal-dual combinatorial relaxation algorithms for computing the maximum degree of subdeterminants. SIAM J. Sci. Comput. 17, 993-1012
14. Murota, K. (1985): Use of the concept of physical dimensions in the structural approach to systems analysis. Japan J. Appl. Math. 2, 471-494
15. Murota, K. (1990): Computing Puiseux-series solutions to determinantal equations via combinatorial relaxation. SIAM J. Comput. 19, 1132-1161
16. Murota, K. (1993): Hierarchical decomposition of symmetric discrete systems by matroid and group theories. Math. Programming 59, 377-404
17. Murota, K. (1995): Computing the degree of determinants via combinatorial relaxation. SIAM J. Comput. 24, 765-796
18. Murota, K. (1995): Combinatorial relaxation algorithm for the maximum degree of subdeterminants: Computing Smith-McMillan form at infinity and structural indices in Kronecker form. Appl. Algebra Engin. Comm. Comput. 6, 251-273
19. Murota, K. (1995): Finding optimal minors of valuated bimatroids. Appl. Math. Lett. 8, 37-42
20. Murota, K. (1996): Valuated matroid intersection I: optimality criteria. SIAM J. Discrete Math. 9, 545-561
21. Murota, K. (1996): Valuated matroid intersection II: algorithms. SIAM J. Discrete Math. 9, 562-576
22. Murota, K. (1996): Convexity and Steinitz's exchange propery. Adv. Math. 124, 272-311
23. Murota, K. (1997): Characterizing valuated delta-matroids as a family of delta-matroids. J. Oper. Res. Soc. Japan 40, 565-578
24. Murota, K. (1999): On the degree of mixed polynomial matrices. SIAM J. Matrix Anal. Appl. 20, 196-227
25. Murota, K. (2000): Matrices and Matroids for Systems Analysis. Algorithms and Combinatorics 20, Springer
26. Murota, K., Iri, M. (1985): Structural solvability of systems of equations - A mathematical formulation for distinguishing accurate and inaccurate numbers in structural analysis of systems. Japan J. Appl. Math. 2, 247-271
27. Murota, K., van der Woude, J.W. (1991): Structure at infinity of structured descriptor systems and its applications. SIAM J. Control Optim. 29, 878-894
28. Pantelides, C.C. (1988): The consistent initialization of differential-algebraic systems. SIAM J. Sci. Stat. Comput. 9, 213-231
29. Svaricek, F. (1990): An improved graph theoretic algorithm for computing the structure at infinity of linear systems. Proceedings of the 29th Conference on Decision and Control, 2923-2924
30. Ungar, J., Kröner, A., Marquardt, W. (1995): Structural analysis of differential-algebraic equation systems - Theory and application. Comput. Chem. Engin. 19, 867-882
31. van der Woude, J.W. (1991): On the structure at infinity of a structured system. Linear Algebra Appl. 148, 145-169