Computation of the GCD of polynomials using gaussian transformations and shifting

References

• BARNETT , S. , 1971 , Greatest common divisor of several polynomials . Proceedings of Cambridge Philosophical Society 70 , 263 – 268 ; 1981, Generalized polynomials and linear systems theory. 3rd IMA Conference on Control Theory, edited by J. E. Marshall et al. (Academic Press) pp. 3–30 .
   Google Scholar
• BLANKISHIP , P. , 1963 , A new version of Euclid Algorithm . American Mathematics Monthly , 70 , 742 – 744 .
   Web of Science ®Google Scholar
• CAULIER , F. M. , and DESOER , C. A. , 1982 , Multivariate Feedback Systems ( New York : Springer-Verlag ).
   Google Scholar
• FOSTER , L. , 1986 , Rank and null space calculations using matrix decomposition without column interchanges . Linear Algebra and its Applications 74 , 47 – 71 .
   Web of Science ®Google Scholar
• GANTMACHER , F. , 1959 , The Theory of Matrices , Vol. 1 ( New York : Chelsea ).
   Google Scholar
• HORN , R. , and JOHNSON , C. , 1985 , Matrix Analysis ( Cambridge : Cambridge University Press ).
   Google Scholar
• KAILATH , T. , 1980 , Linear Systems ( Englewood Cliffs , NJ : Prentice Hall ).
   Google Scholar
• KAHCANIAS , N. , 1987 , Invariance properties and characterisation of the greatest common divisor of a set of polynomials . International Journal of Control 46 , 1751 – 1760 ; 1989, System theoretic characterisations of the greatest common divisor of a set of polynomials. Applications of Matrix Theory, edited by M. J. C. Gover and S. Barnett, IMA Conference Series (Clarendon Press), pp. 237–248.
   Web of Science ®Google Scholar
• KARCANIAS , N. , GIANNAKOPOULOS , C. , and HUBBARD , M. , 1983 , Almost zeros of a set of polynomials of R[s] . International Journal of Control , 38 , 1213 – 1238 .
   Web of Science ®Google Scholar
• MARCUS , M. , and MINC , H. , 1964 , A Survey of Matrix Theory and Matrix Inequalities ( Boston : AHyn and Bacon ).
   Google Scholar
• MITROULI , M. , 1991 , Numerical issues and computational problems in algebraic control theory . Ph.D. thesis , City University , London , U.K .
   Google Scholar
• MITROULI , M. , and KARCANIAS , N. , 1991 , Lists of programs for exterior and nongeneric computations. Control Engineering Centre, Research Report , City University , CEC/MM-NK-102 , London , U.K .
   Google Scholar
• PACE , I.S. , and BARNETT , S. , 1973 , Comparison of algorithms for calculation of GCD of polynomials . International Journal of Systems Science , 4 , 211 – 226 .
   Web of Science ®Google Scholar
• ROSENUROCH , H. H. , 1970 , State-Space and Multivariable Theory ( New York : Wiley ).
   Google Scholar
• VARDULAKIS , A. I. G. , and STOYLE , P. N. R. , 1978 , Generalized resultant theorem . Journal of the Institute of Mathematics and its Applications , 22 , 331 – 335 .
   Google Scholar
• WILKINSON , J. H. , 1963 , Rounding Errors in Algebraic Processes ( London : HMSO ); 1965, The Algebraic Eigenvalue Problem (Oxford Oxford University Press) .
   Google Scholar
• WONHAM , W. M. , 1979 , Linear Multivariable Control a Geometric Approach , second edition ( New York : Springer-Verlag ).
   Google Scholar