Computing the degrees of al l cofactors in mixed polynomial matrices

SIAM Journal on Discrete Mathematics

Volumn 23, Issue 2, 2009, Pages 647-660

  Iwata, Satoru ^a   Takamatsu, Mizuyo ^b  

^a KYOTO UNIVERSITY   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Combinatorial matrix theory; Degree of cofactor; Mixed matrix; Polynomial matrix; Valuated matroid

Indexed keywords

ALL-PAIR SHORTEST PATH; COFACTORS; COMBINATORIAL MATRIX THEORY; CONSERVATION LAW; DIFFERENTIAL ALGEBRAIC EQUATIONS; HYBRID ANALYSIS; INDEPENDENT PARAMETERS; MATROID INTERSECTION; MATROIDS; MIXED MATRIX; MIXED POLYNOMIALS; NON-ZERO COEFFICIENTS; PHYSICAL CHARACTERISTICS; POLYNOMIAL MATRICES; RUNNING TIME;

CIRCUIT SIMULATION; COMPUTATION THEORY; DIFFERENTIAL EQUATIONS; POLYNOMIALS;

MATRIX ALGEBRA;

EID: 73349085864     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/070706021     Document Type: Article

References (16)

1. K. E. BRENAN, S. L. CAMPBELL, AND L. R. PETZOLD, Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, SIAM, Philadelphia, 1996.
2. P. BUJAKIEWICZ, Maximum Weighted Matching for High Index Differential Algebraic Equations, Doctor's dissertation, Delft University of Technology, Delft, The Netherlands, 1994.
3. P. BUJAKIEWICZ AND P. P. J. VAN DEN BOSCH, Determination of perturbation index of a DAE with maximum weighted matching algorithm, in Proceedings of the IEEE/IFAC Joint Symposium on Computer-Aided Control System Design, 1994, pp. 129-136.
4. A. W. M. DRESS AND W. WENZEL, Valuated matroids, Adv. Math., 93 (1992), pp. 214-250.
5. R. W. FLOYD, Algorithm 97 - shortest path, Communications of the ACM, 5 (1962), p. 345.
6. H. N. GABOW AND Y. Xu, Efficient theoretic and practical algorithms for linear matroid intersection problems, J. Comput. System Sci., 53 (1996), pp. 129-147.
7. M. IRI AND N. TOMIZAWA, An algorithm for finding an optimal "independent assignment," J. Oper. Res. Soc. Japan, 19 (1976), pp. 32-57.
8. S. IWATA AND K. MUROTA, Combinatorial relaxation algorithm for mixed polynomial matrices, Math. Program., 90 (2001), pp. 353-371.
9. S. IWATA AND M. TAKAMATSU, Index minimization of differential-algebraic equations in hybrid analysis for circuit simulation, Math. Program., to appear.
10. K. MUROTA, Use of the concept of physical dimensions in the structural approach to systems analysis, Japan J. Appl. Math., 2 (1985), pp. 471-494.
11. K. MUROTA, Valuated matroid intersection I: Optimality criteria,SIAMJ.DiscreteMath., 9 (1996), pp. 545-561.
12. K. MUROTA, Valuated matroid intersection II: Algorithms, SIAM J. Discrete Math., 9 (1996), pp. 562-576.
13. K. MUROTA, On the degree of mixed polynomial matrices, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 196-227.
14. K. MUROTA, Matrices and Matroids for Systems Analysis, Springer-Verlag, Berlin, 2000.
15. K. MUROTA AND M. IRI, Structural solvability of systems of equations - A mathematical formulation for distinguishing accurate and inaccurate numb ers in structural analysis of systems, Japan J. Appl. Math., 2 (1985), pp. 247-271.
16. S. WARSHALL, A theorem on Boolean matrices, J. ACM, 9 (1962), pp. 11-12.