Approximate GCD in Bernstein basis
Robert M. Corless, Leili Rafiee Sevyeri · Communications in computer and information science · 2019
In general, finding the Greatest Common Divisor (GCD) of two exactly-known univariate polynomials is a well understood problem. However, it is also known that the GCD problem for noisy polynomials (polynomials with errors in their coefficients) is ill-posed. More precisely, a small error in coefficients of polynomials P and Q with a non-trivial GCD generically leads to a constant GCD. We note that the choice of basis makes no difference to this difficulty.