Optimizing gaussian quadrature for positive definite strong moment functionals

摘要

Classical Gaussian quadrature is anchored in the space of real polynomials at polynomial degree 0 and is monotonically directed by successively increasing polynomial degree. The results of recent research, investigating weighing anchor and charting various courses in search of the best currents in the space of real Laurent polynomials, are presented. Standard error bound minimization anchoring and steering algorithms which utilize the moments of positive definite strong moment functionals to guide the construction of ordered orthogonal Laurent polynomial sequences are introduced.