We propose a modification of the GPGCD algorithm, which has been presented in our previous research, for calculating approximate greatest common divisor (GCD) of more than 2 univariate polynomials with real coefficients and a given degree. In transferring the approximate GCD problem to a constrained minimization problem, different from the original GPGCD algorithm for multiple polynomials which uses the Sylvester subresultant matrix, the proposed algorithm uses the Bézout matrix. Experiments show that the proposed algorithm is more efficient than the original GPGCD algorithm for multiple polynomials with maintaining almost the same accuracy for most of the cases.
With the progress of algebraic computations on polynomials and matrices, we are paying more attention to approximate algebraic algorithms. Among approximate algebraic algorithms, those for calculating approximate greatest common divisor (GCD) consider a pair of given polynomials
f
and
g
that are relatively prime in general, and find f and g which are close to
f
and
g
, respectively, in the sense of polynomial norm, and have the GCD of certain degree. The algorithms can be classified into two categories: 1) for a given tolerance (magnitude) of ||
f
- f|| and ||
g
- g||, make the degree of approximate GCD as large as possible, and 2) for a given degree
d
, minimize the magnitude of ||
f
- f|| and ||
g
- g||.
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