On Computing the Exact Determinant of Matrices with Polynomial Entries

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On Computing the Exact Determinant of Matrices with Polynomial Entries

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Journal of the ACM (JACM) archive
Volume 22 , Issue 1 (January 1975) table of contents

Pages: 38 - 50

Year of Publication: 1975

ISSN:0004-5411

Authors

E. Horowitz	Computer Science Program, University of Southern California, Los Angeles, CA
S. Sahni	Department of Computer, Information and Control Sciences, University of Minnesota, Minneapolis, MN

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 1, Downloads (12 Months): 37, Citation Count: 9

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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	BAREISS, E. H. Sylvester's identity and multistep integer-preserving Gaussian ehmination. Math Compt. 22, 103 (july 1968), 565-578.
	2	BAR~ISS, E. H Computational solutions of matrix problems over an integral domain. J. Inst. Math. and Appls. 10 (1972), 68-104.
	3	BAREISS, E. H., AND MAZUKELLI, D Multmtep elimination over commutative rings. Argonne National Lab Rep. ANL-7898, April 1972.
	4	Stanley Cabay, Exact solution of linear equations, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.392-398, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806310]
	5	George E. Collins, The SAC-1 system: An introduction and survey, Proceedings of the second ACM symposium on Symbolic and algebraic manipulation, p.144-152, March 23-25, 1971, Los Angeles, California, United States [doi>10.1145/800204.806279]
	6	DORR, F W. An example of ill-conditioning in the numemcal solution of singular perturbation problems Math. Comput. 25,114 (April 1971), 271-284.
	7	W. M. Gentleman , S. C. Johnson, Analysis of algorithms, a case study: Determinants of polynomials, Proceedings of the fifth annual ACM symposium on Theory of computing, p.135-141, April 30-May 02, 1973, Austin, Texas, United States [doi>10.1145/800125.804044]
	8	HonowiTz, E. The efficient calculation of powers of a polynomial. J. Comput. ,Syst. Sc~. 7, 5 (Oct. 1973), 469-481.
	9	HOROWITZ, E., AND SAnNI, S. On computing the determinant of matrices with polynomial entries. Comput Scl Tit 73-180, Cornell U, Ithaca, N Y, June 1973.
	10	HOWELL, J., AND GREGORY, R. T Solving systems of linear algebraic equations using residue arithmetic I, II, and III. BIT 9 (1969), 200-224, 324-337, and BIT 10 (1970), 23-27.
	11	ISAACSON, E , ANn KELLER, H. B Analys~s of Numemcal Methods Wiley, New York, 1966.
	12	KNtTTtt, D. E The Art of Computer Programming, Vol. 2: Semznumerwal Algorithms. Addison- Wesley, Reading, Mass., 1969.
	13	LIPsoN, J. D Symbolic methods for the computer solution of linear equations with apphcations to flow graphs Proc of the 1968 Summer Institute on Symbolic Mathematmal Computatmn, IBM, Boston, June 1969, pp 233-303.
	14	Michael T. McClellan, The Exact Solution of Systems of Linear Equations with Polynomial Coefficients, Journal of the ACM (JACM), v.20 n.4, p.563-588, Oct. 1973 [doi>10.1145/321784.321787]

CITED BY 9

	Tateaki Sasaki , Hirokazu Murao, Efficient Gaussian Elimination Method for Symbolic Determinants and Linear Systems, ACM Transactions on Mathematical Software (TOMS), v.8 n.3, p.277-289, Sept. 1982
	Michael T. McClellan, A Comparison of Algorithms for the Exact Solution of Linear Equations, ACM Transactions on Mathematical Software (TOMS), v.3 n.2, p.147-158, June 1977
	Michael T. McClellan, The Exact Solution of Linear Equations with Rational Function Coefficients, ACM Transactions on Mathematical Software (TOMS), v.3 n.1, p.1-25, March 1977
	Martin L. Griss, An efficient sparse minor expansion algorithm, Proceedings of the annual conference, p.429-434, October 20-22, 1976, Houston, Texas, United States
	S. Cabay , T. P. L. Lam, Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations, ACM Transactions on Mathematical Software (TOMS), v.3 n.4, p.386-397, Dec. 1977
	Martin L. Griss, The Algebraic Solution of Sparse Linear Systems via Minor Expansion, ACM Transactions on Mathematical Software (TOMS), v.2 n.1, p.31-49, March 1976
	Stanley Cabay , Bart Domzy, Systems of linear equations with dense univariate polynomial coefficients, Journal of the ACM (JACM), v.34 n.3, p.646-660, July 1987
	Paul S. Wang , Tadatoshi Minamikawa, Taking advantage of zero entries in the exact inverse of sparse matrices, Proceedings of the third ACM symposium on Symbolic and algebraic computation, p.346-350, August 10-12, 1976, Yorktown Heights, New York, United States
	J. Smit, A cancellation free algorithm, with factoring capabilities, for the efficient solution of large sparse sets of equations, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.146-154, August 05-07, 1981, Snowbird, Utah, United States