scholarly journals Barnett’s Theorems About the Greatest Common Divisor of Several Univariate Polynomials Through Bezout-like Matrices

2002 ◽  
Vol 34 (1) ◽  
pp. 59-81 ◽  
Author(s):  
Gema M. Diaz-Toca ◽  
Laureano Gonzalez-Vega
Keyword(s):  
Greatest Common Divisor ◽  
Univariate Polynomials

scholarly journals Numerical methods for computing the greatest common divisor of univariate polynomials using floating point arithmetic

2019 ◽  
Vol 60 ◽  
pp. C127-C139
Author(s):  
Markus Hegland
Keyword(s):  
Polynomial Equation ◽  
Polynomial Systems ◽  
Floating Point ◽  
Greatest Common Divisor ◽  
Close Monitoring ◽  
Acceptable Result ◽  
Floating Point Arithmetic ◽  
Univariate Polynomials ◽  
Value Decomposition ◽  
Point Arithmetic

Computing the greatest common divisor (GCD) for two polynomials in floating point arithmetic is computationally challenging and even standard library software might return the result GCD=1 even when the polynomials have a nontrivial GCD. Here we review Euclid's algorithm and test a variant for a class of random polynomials. We find that our variant of Euclid's method often produces an acceptable result. However, close monitoring of the norm of the vector of coefficients of the intermediate polynomials is required. References R. M. Corless, P. M. Gianni, B. M. Trager, and S. M. Watt. The singular value decomposition for polynomial systems. In Proceedings of the 1995 International Symposium on Symbolic and Algebraic Computation, ISSAC '95, pages 195207. ACM, 1995. doi:10.1145/220346.220371. H. J. Stetter. Numerical polynomial algebra. SIAM, 2004. doi:10.1137/1.9780898717976. Z. Zeng. The numerical greatest common divisor of univariate polynomials. In Randomization, relaxation, and complexity in polynomial equation solving, volume 556 of Contemp. Math., pages 187217. Amer. Math. Soc., 2011. doi:10.1090/conm/556/11014.

Greatest common divisor of matrices one of which is a disappear matrix

2014 ◽  
Vol 66 (3) ◽  
pp. 479-485 ◽  
Author(s):  
A. M. Romaniv ◽  
V. P. Shchedryk
Keyword(s):  
Greatest Common Divisor
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