2017/04/27 by Teresa Cortadellas, Teresa, Cortadellas, Carlos D'Andrea +3
Computer Science · Engineering · #13P05 #14Q15 #68W30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Numerical Methods and Algorithms #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1704.08563
openalex publication_date 2017/04/27 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28
We describe geometrically and algebraically the set of unattainable points\nfor the Rational Hermite Interpolation Problem (i.e. those points where the\nproblem does not have a solution). We show that this set is a union of\nequidimensional complete intersection varieties of odd codimension, the number\nof them being equal to the minimum between the degrees of the numerator and\ndenominator of the problem. Each of these equidimensional varieties can be\nfurther decomposed as a union of as many rational (irreducible) varieties as\ninput data points. We exhibit algorithms and equations defining all these\nobjects.\n