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Results tagged with quadrature
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user 171738
2
votes
1
answer
868
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Error in Gauss-Laguerre numerical quadrature scheme
The $n$-th Gauss-Laguerre quadrature scheme aims to approximate integral of exponentially decreassing function over $[0 ; \infty[$ by a finite sum, according to:
$$ \int _0
^{+ \infty} … Uspenksy, On the convergence of quadrature formulas related to an infinite interval, Trans. Amer. Math. …
- 97
1
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Gaussian quadrature, with no exact result over polynomial, but on inverse functions
H., Secrest D., "Gaussian Quadrature Formulas". Prentice-Hall, Englewood Cliffs, N.J., 1966
gives some answer to my question. … .$$
In section 3.2.3 "Semi-infinite to Finite segment", a quadrature over $]0, 1]$ is construted to be exact for functions
$$ t \longrightarrow \displaystyle { \sum _{k = 1} ^M a_k (\ln x)^k } \ .$$ …
- 97
1
vote
0
answers
90
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Explicit growth rate estimation of Gauss-Laguerre quadrature
In particular, I want to understand the error $\varepsilon_n(f)$ produced by the $n$-th degree Gauss-Laguerre quadrature. … Uspenksy, On the convergence of quadrature formulas related
to an infinite interval, Trans. Amer. Math. …
- 97
0
votes
1
answer
391
views
Gaussian quadrature, with no exact result over polynomial, but on inverse functions
Generally, a Gaussian quadrature of degree $n$ over an interval $I$ is defined so that it integrates exactly polynomials up to degree $2n - 1$. The main tool are the orthogonal polynomials. … For example, the space $\mathbb{R} \left [\dfrac{1}{X} \right ]$ could be useful to develop quadratures over $[1 ; + \infty[$, i.e. a quadrature rule
$$ \int _1 ^{+ \infty}
\omega(x) f(x) …
- 97