Algorithm 767: a Fortran 77 package for column reduction of polynomial matrices

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Algorithm 767: a Fortran 77 package for column reduction of polynomial matrices

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 23 , Issue 1 (March 1997) table of contents

Pages: 111 - 129

Year of Publication: 1997

ISSN:0098-3500

Authors

A. J. Geurts	Eindhoven Univ. of Technology, Eindhoven, The Netherlands
C. Praagman	Univ. of Groningen, Groningen, The Netherlands

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 6, Downloads (12 Months): 47, Citation Count: 0

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appendices and supplements references index terms review collaborative colleagues peer to peer

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APPENDICES and SUPPLEMENTS

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A {Fortran} 77 Package for Column Reduction of Polynomial Matrices

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	E. Anderson , Z. Bai , C. Bischof , J. Demmel , J. Dongarra , J. Du Croz , A. Greenbaum , S. Hammarling , A. McKenney , S. Ostrouchov , D. Sorensen, LAPACK's user's guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992
	2	BEELEN, TH. G.g. 1987. New algorithms for computing the Kronecker structure of a pencil with applications to systems and control theory. Ph.D. thesis, Eindhoven Univ. of Technology, Eindhoven, The Netherlands.
	3	Th. G. J. Beelen , G. J. van den Hurk , C. Praagman, A new method for computing a column reduced polynomial matrix, Systems & Control Letters, v.10 n.4, p.217-224, April 1988 [doi>10.1016/0167-6911(88)90010-2]
	4	CODENOTTI, B. AND LOTTI, G. 1989. A fast algorithm for the division of two polynomial matrices. IEEE Trans. Autom. Contr. 34, 446-448.
	5	Jack J. Dongarra , Jeremy Du Croz , Sven Hammarling , Richard J. Hanson, An extended set of FORTRAN basic linear algebra subprograms, ACM Transactions on Mathematical Software (TOMS), v.14 n.1, p.1-17, March 1988 [doi>10.1145/42288.42291]
	6	GEURTS, A. J. AND PRAAGMAN, C. 1994. A Fortran subroutine for column reduction of polynomial matrices. EUT Rep. 94-WSK-01, Eindhoven Univ. of Technology, Eindhoven, The Netherlands.
	7	INOUYE, I. 1979. An algorithm for inverting polynomial matrices. Int. J. Contr. 30, 989-999.
	8	KAILATH, T. 1980. Linear Systems. Prentice-Hall, Englewood Cliffs, N.J.
	9	C. L. Lawson , R. J. Hanson , D. R. Kincaid , F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.308-323, Sept. 1979 [doi>10.1145/355841.355847]
	10	Ching-An Lin , Chien-Wen Yang , Tung-Fu Hsieh, An algorithm for inverting rational matrices, Systems & Control Letters, v.27 n.1, p.47-53, Jan. 31, 1996 [doi>10.1016/0167-6911(95)00043-7]
	11	NEVEN, W. H.L. 1988. Polynomial methods in systems theory. Master's thesis, Eindhoven Univ. of Technology, Eindhoven, The Netherlands.
	12	NEVEN, W. H. L. AND PRAAGMAN, C. 1993. Column reduction of polynomial matrices. Lin. Alg. Appl. 188-189, 569-589.
	13	C. Praagman, Inputs, outputs and states in the representation of time series, Analysis and optimization of systems, Springer-Verlag, London, 1988
	14	PRAAGMAN, C. 1991. Invariants of polynomial matrices. In Proceedings of the 1st ECC, I. Landau, Ed. INRIA, France, 1274-1277.
	15	VAN DOOREN, P. 1979. The computation of Kronecker's cononical form of a singular pencil. Lin. Alg. Appl. 27, 103-140.
	16	WANG, Q. G. AND ZHOU, C.H. 1986. An efficient division algorithm for polynomial matrices. IEEE Trans. Autom. Contr. 31, 165-166.
	17	WGS. 1990. SLICOT: Implementation and documentation standards. WGS Rep. 90-01. Working Group on Software, Eindhoven, The Netherlands.
	18	J C Willems, From time series to linear system-part I. Finite dimensional linear time invariant systems, Automatica (Journal of IFAC), v.22 n.5, p.561-580, Sept. 1986 [doi>10.1016/0005-1098(86)90066-X]
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	25	ZHANG, S.Y. 1986. The division of polynomial matrices. IEEE Trans. Autom. Contr. 31, 55-56.
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INDEX TERMS

Primary Classification:
F. Theory of Computation
F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
F.2.1 Numerical Algorithms and Problems
Subjects: Computations on matrices

General Terms:
Algorithms, Reliability

Keywords:
Fortran subroutine, column reduction

REVIEW

"Hale F. Trotter : Reviewer"

Consider matrices whose entries are polynomials in one variable with real coefficients. The leading column coefficient matrix of a polynomial matrix R is formed by replacing each polynomial entry more...

Collaborative Colleagues:

A. J. Geurts: colleagues

C. Praagman: colleagues

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