Seminar in Numerical Analysis: Walter Gautschi (Purdue University)

Repeated modifications of orthogonal polynomials by linear divisors

Algorithms are developed for computing the coefficients in the three-term recurrence relation of repeatedly modified orthogonal polynomials, the modifications involving division of the orthogonality measure by a linear function with real or complex coefficient. The respective Gaussian quadrature rules can be used to account for simple or multiple poles that may be present in the integrand. Several examples are given to illustrate this.

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