Iteration-Free Computation of Gauss-Legendre Quadrature Nodes and Weights

Gauss-Laguerre Quadrature Evaluation Points and Weights — MATLAB {amp} Simulink Example


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[1]  2015/02/15 22:47   Male / 50 years old level / A teacher / A researcher / Very /

Is teh code public ? I would like to see it as I am interested to see if it is ok for n{amp}gt;100 and possibliy adapt it.

[2]  2015/02/11 09:38   Male / 60 years old level or over / A teacher / A researcher / Very /

Purpose of use
numerically solving an initial value problem of a hyperbolic 4×4-system of PDE-s

[3]  2013/10/18 20:26   Male / 60 years old level or over / A teacher / A researcher / Very /

Purpose of use
Checking precision of gauss-laguerre nodes and weights at 38 digits.
They are good at quad-precision( 35 digits)
the display on screen truncates the third column of this calculation due
to lack of page space. In such cases can you extend the page or shift some
columns to another page?
However I tried «copy and paste» of the table to another editor and there I
was able to see all the columns in full.
Thank you

[4]  2012/02/28 01:52   Male / 30 years old level / A student / Very /

I can integrate the Gauss-Laguerre Integral with an alpha {amp}lt; -1 (for example alpha = -1.8) but I cannot obtain weights!

[5]  2011/08/24 13:11   Male / 30 years old level / A teacher / A researcher / Very /

Purpose of use
Lecture for students.
That is a great page.
alpha = 

(-σ3 σ15 σ2-σ6-σ12-σ11-σ10 6root(σ16,z,1)-root(σ16,z,2) σ1 σ4-σ2-root(σ16,z,1)2σ1 σ4 σ2-σ7-σ13-σ11-σ10 6root(σ16,z,2)-root(σ16,z,1) root(σ16,z,2)-root(σ16,z,3) root(σ16,z,2)-root(σ16,z,4)σ5 σ4 σ15-σ8-σ13-σ12-σ10 6root(σ16,z,3)-root(σ16,z,4) σ5-σ1-σ3 root(σ16,z,3)2-σ5 σ1 σ3-σ9-σ13-σ12-σ11 6σ14 root(σ16,z,1) σ14 root(σ16,z,2) σ14 root(σ16,z,3)-root(σ16,z,4)3 σ9-σ8-σ7-σ6)where  σ1=root(σ16,z,1) root(σ16,z,3)  σ2=root(σ16,z,3) root(σ16,z,4)  σ3=root(σ16,z,2) root(σ16,z,3)  σ4=root(σ16,z,1) root(σ16,z,4)  σ5=root(σ16,z,1) root(σ16,z,2)  σ6=root(σ16,z,2) root(σ16,z,3) root(σ16,z,4)  σ7=root(σ16,z,1) root(σ16,z,3) root(σ16,z,4)  σ8=root(σ16,z,1) root(σ16,z,2) root(σ16,z,4)  σ9=root(σ16,z,1) root(σ16,z,2) root(σ16,z,3)  σ10=2 root(σ16,z,4)  σ11=2 root(σ16,z,3)  σ12=2 root(σ16,z,2)  σ13=2 root(σ16,z,1)  σ14=root(σ16,z,4)2  σ15=root(σ16,z,2) root(σ16,z,4)  σ16=z4-16 z3 72 z2-96 z 24

Exponentially-fitted Gauss–Laguerre quadrature rule for integrals over an unbounded interval

New quadrature formulae are introduced for the computation of integrals over the whole positive semiaxis when the integrand has an oscillatory behaviour with decaying envelope. The new formulae are derived by exponential fitting, and they represent a generalization of the usual Gauss–Laguerre formulae. Their weights and nodes depend on the frequency of oscillation in the integrand, and thus the accuracy is massively increased. Rules with one up to six nodes are treated with details. Numerical illustrations are also presented.

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