High-order generalized Gauss-Radau and Gauss-Lobatto formulae for Jacobi and Laguerre weight functions

摘要

The generation of generalized Gauss-Radau and Gauss-Lobatto quadrature formulae by methods developed by us earlier breaks down in the case of Jacobi and Laguerre measures when the order of the quadrature rules becomes very large. The reason for this is underflow resp. overflow of the respective monic orthogonal polynomials. By rescaling of the polynomials, and other corrective measures, the problem can be circumvented, and formulae can be generated of orders as high as 1,000.