Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis

Abstract

In this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree M that approximates a polynomial of degree N>Mon a symmetric interval for the L2-norm. We also formally prove that using the formula is more computationally efficient than using a classical matrix multiplication approach and we provide an example to illustrate that it is more numerically stable than the classical approach.

Keywords

• Polynomial degree reduction
• Legendre polynomials
• Optimization
• Euclidian norm
• Canonical basis