11
votes
Accepted
Is quadrature still considered part of numerical analysis?
Math journals that have recently published papers on "quadrature" include
Applied Numerical Mathematics
IMA Journal of Numerical
Analysis
Journal of Approximation Theory
Journal of ...
- 188k
6
votes
Is quadrature still considered part of numerical analysis?
This question cannot be answered without knowing more about your preprint and the specific journal. As a few rules of thumb:
Much of "numerical mathematics" has been numerical mathematics ...
- 5,327
4
votes
Integrating powers without much calculus
I think it is also worth looking at the case $p=-1$, in the spirit of your context. It also provides a nice way to introduce the logarithm and the exponential function (quite closely to the ...
- 60.5k
4
votes
Quadrature for numerical integration over infinite intervals
I would convert the integration range to a finite interval,
$$\int_{-\infty}^\infty f(x)dx=\int_0^1\left[f(1/t-1)+f(-1/t+1)\right]t^{-2}dt,$$ and then use an adaptive Gauss-Kronrod routine. Many ...
- 188k
2
votes
Clenshaw-Curtis integration without Fourier
In "Error bounds for the Clenshaw-Curtis quadrature formulas" the error bounds are obtained without relying on analytic function theory (and no Fourier transforms).
- 188k
2
votes
Accepted
Integrating a B-Spline basis function with respect to the standard normal PDF
Since a B-spline is a piecewise polynomial function, the question is whether there exists an exact equality formula for the integral $\int_{-a}^{b}u^pe^{-u^2/2}du$. This integral equals an elementary ...
- 188k
2
votes
Error in Gauss-Laguerre numerical quadrature scheme
The function $f(x)=e^{-x+\sqrt{x}}$ belongs to the space $C_{0}^{3}[0,\infty)$ defined, for $q\geq p\geq0$, by
$$C _ { p } ^ { q } [ 0,\infty ) : = \{ f \in C ^ { p } [ 0,\infty ) \cap C ^ { q } ( 0,\...
- 4,034
1
vote
Gaussian quadrature, with no exact result over polynomial, but on inverse functions
The book
Stroud A. H., Secrest D., "Gaussian Quadrature Formulas". Prentice-Hall, Englewood Cliffs, N.J., 1966
gives some answer to my question.
See Section 3.2.2 "Finite to semi-...
- 97
1
vote
Accepted
Proof Reference - Polynomial interpolation at quadrature points
Here, three possible references for the formula:
P. J. Davis and P. Rabinowitz, Methods of Numerical Integration,
Computer Science and Applied Mathematics. Academic Press, New York,
1984 (see p....
- 4,034
1
vote
Numerical Computation of Orthogonal Polynomials Recurrence Relations
Computation of the coefficients of the recurrence relations of orthogonal polynomials is studied in details in the standart reference:
Gautschi, W., Orthogonal polynomials: computation and ...
- 4,034
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