# abscissas

(0.000 seconds)

## 4 matching pages

##### 1: 18.40 Methods of Computation
###### 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 $w(x)$, 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 $N$ be a positive integer and define …The quadrature abscissas $x_{n}$ and weights $w_{n}$ 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 $w(x)$. …
##### 2: 3.3 Interpolation
###### §3.3(i) Lagrange Interpolation
The nodes or abscissas $z_{k}$ are real or complex; function values are $f_{k}=f(z_{k})$. …
##### 3: 18.38 Mathematical Applications
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. …
##### 4: 18.39 Applications in the Physical Sciences
Full expressions for both $A_{x_{i},l}$ and $B_{l}(x)$ are given in Yamani and Reinhardt (1975) and it is seen that $|\ifrac{A_{x_{i},l}}{B_{l}(x_{i})}|^{2}$ = $\ifrac{w_{i}^{N}}{w^{\mathrm{CP}}(x_{i})}$ where $w^{N}_{i}$ is the Gaussian-Pollaczek quadrature weight at $x=x_{i}$, and $w^{\mathrm{CP}}(x_{i})$ is the Gaussian-Pollaczek weight function at the same quadrature abscissa. …