Approximate GCD by bernstein basis, and its applications

Abstract

For the given pair of univariate polynomials generated by empirical data hence with a priori error on their coefficients, computing their greatest common divisor can be done by several known approximate GCD algorithms that are usually for polynomials represented by the power polynomial basis (power form). Recently, there are studies on approximate GCD of polynomials represented by not the power polynomial basis, and especially the Bernstein polynomial basis (Bernstein form) is one of them. we are interested in computing approximate GCD of polynomials in the power form but their perturbation is measured by the Euclidean norm of perturbation in the Bernstein form, and we introduce its applications for computing a reduced rational function, the rational function approximation and Pade approximation to get a better approximation in L2-norm on [0, 1].