On the Computation of Recurrence Coefficients for Univariate Orthogonal Polynomials

Associated to a finite measure on the real line with moments are recurrence coefficients in three-term formula for orthogonal polynomials respect this measure. These frequently inputs modern computational tools that facilitate evaluation and manipulation of measure, such tasks foundational numerical approximation quadrature. Although classical measures known explicitly, those nonclassical must typically be numerically computed. We survey review existing approaches computing these univariate polynomial families propose novel “predictor–corrector” algorithm general class continuous measures. combine predictor–corrector scheme stabilized Lanczos procedure new hybrid computes fairly wide can have both discrete parts. evaluate algorithms against methods terms accuracy efficiency.