Minimal solutions of the rational interpolation problem

2018/08/07 by Benitez, Teresa Cortadellas, D'Andrea, Carlos, Montoro, Eulalia
#Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.1808.02575

Abstract

We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies with the standard method provided by the Extended Euclidean Algorithm. As a consequence, we obtain explicit descriptions for solutions of "minimal" degrees in terms of the degrees of elements appearing in the EEA. This allows us to describe the minimal degree in a μ-basis of a polynomial planar parametrization in terms of a "critical" degree arising in the EEA.

Related

• The Spectral Basis and Rational Interpolation
• Observations on interpolation by total degree polynomials in two variables
• On the Complexity of Interpolation by Polynomials with Non-negative Real Coefficients
• Interpolation of Varieties of Minimal Degree
• Optimal Point Sets for Total Degree Polynomial Interpolation in Moderate\n Dimensions