Constrained multi-degree reduction with respect to Jacobi norms

• We study the problem of constrained degree reduction with respect to Jacobi norms.
• Our results generalize several previous findings on polynomial degree reduction.
• We explore the space of Jacobi parameters on the reduced polynomial approximation.

We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2L2-norm is presented.