- Full text PDF available (34)
- This year (2)
- Last 5 years (12)
- Last 10 years (36)
Journals and Conferences
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)
We give examples of problem areas in interpolation, approximation, and quad-rature, that call for orthogonal polynomials not of the classical kind. We then discuss numerical methods of computing the respective Gauss-type quadrature rules and orthogonal polynomials. The basic task is to compute the coefficients in the three-term recurrence relation for the… (More)
We develop a computational procedure, based on Taylor's series and continued fractions, for evaluating Tncomi's incomplete gamma functmn 7*(a, x) = (x-"/F(a))S~ e-~t'-ldt and the complementary incomplete gamma function F(a, x) = $7 e-tt "-1 dt, suitably normalized, m the region x >_. 0,-oo < a < oo.
Orthogonal polynomials relative to the Jacobi weight function, but orthogonal on a strict subinterval of [ − 1, 1], are studied, in particular with regard to their numerical computation. Related Gaussian quadrature rules are also considered.
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  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)
Quadrature problems involving functions that have poles outside the interval of integration can prootably be solved by methods that are exact not only for poly-nomials of appropriate degree, but also for rational functions having the same (or the most important) poles as the function to be integrated. Constructive and computational tools for accomplishing… (More)