abscissas
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1: 18.40 Methods of Computation
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A numerical approach to the recursion coefficients and quadrature abscissas and weights
… ►These quadrature weights and abscissas will then allow construction of a convergent sequence of approximations to , as will be considered in the following paragraphs. … ►A simple set of choices is spelled out in Gordon (1968) which gives a numerically stable algorithm for direct computation of the recursion coefficients in terms of the moments, followed by construction of the J-matrix and quadrature weights and abscissas, and we will follow this approach: Let be a positive integer and define …The quadrature abscissas and weights then follow from the discussion of §3.5(vi). … ►Having now directly connected computation of the quadrature abscissas and weights to the moments, what follows uses these for a Stieltjes–Perron inversion to regain . …2: 3.3 Interpolation
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§3.3(i) Lagrange Interpolation
►The nodes or abscissas are real or complex; function values are . …3: 18.38 Mathematical Applications
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►The basic ideas of Gaussian quadrature, and their extensions to non-classical weight functions, and the computation of the corresponding quadrature abscissas and weights, have led to discrete variable representations, or DVRs, of Sturm–Liouville and other differential operators.
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