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The concern here is with Gauss-type quadrature rules that are exact for a mixture of polynomials and rational functions, the latter being selected so as to simulate poles that may be present in the integrand. The underlying theory is presented as well as methods for constructing such rational Gauss formulae. Relevant computer routines are provided and(More)
A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the three-term recurrence relation satisfied by the orthogonal polynomials. Once these are known,(More)
Much of the work of Golub and his collaborators uses techniques of linear algebra to deal with problems in analysis, or employs tools from analysis to solve problems arising in linear algebra. Instances are described of such interdisciplinary work, taken from quadrature theory, orthogonal polynomials, and least squares problems on the one hand, and error(More)
real proeedure perl (A, n) j integer nj array Aj comment Let A be an n X n real matrix, n > 1. The permanent function of A, denoted per(A), is computed by H. J. Ryser's [1] expansion formula: n-l T per(A) = L (_I)r L II Xi r=O xETn_ri=l where Tj, j = n, n-1, ... ,2, 1, is the set of vectors x = (Xi), i = 1, 2, '" , n which are obtained by adding j columns(More)
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,(More)