Comments on: Numerical Integration

By: Pablo

Pablo — Thu, 16 Feb 2012 17:37:15 +0000

Hi Pavel!

First of all congrats for your excellent job.

I’m currently using your code to integrate the elements of the stiffness matrix in a solver for Poisson Eq using weak form of Finite Elements Method.

The point is that the code works well when I try to evaluate numerically the integral of a function in ‘x’, but I don’t manage to integrate a constant (i.e. imagine we want to do gausslegendre(@(x) 1,-1,1). The result of this operation is, as far as I’m concerned, random.

I could neither do this with the original version of quad.m, but after performing some changes to the code now I’m able to do it with a modified ver called myquad.m

Could it be possible to perform the integration of a constant using your code?

Many thanks and congrats again for your work!

Best regards from El Salvador

Pablo

By: Pavel Holoborodko

Pavel Holoborodko — Tue, 17 Jan 2012 07:47:26 +0000

I completely agree with you, direct root search with good starting point is much faster than eigen-solving Jacobi matrix. I have plans to cover all commonly used quadrature, plus to port QuadPack adaptive integration rules to Matlab. I will release them as a part of Multiprecision Computing Toolbox for MATLAB. It already has Gauss-Legendre and Gauss-Krondrod rules which is the most important for practical applications since it allows re-use of lower order quadrature nodes in higher order rules. Thus saving on function evaluations.

By: Stephen

Stephen — Tue, 17 Jan 2012 06:32:25 +0000

I came across your site while searching for Gauss-Laguerre quadrature. Do you plan to include this in your toolbox? I am currently using the eigen method, but I expect Newton’s method with the initial approximations from Stroud and Secrest would be faster.

By: Ali

Ali — Fri, 13 Jan 2012 15:35:35 +0000

nice job,but I really wants to know how to use it for double integration,if some how it’s doable please let me know?

By: Sergey

Sergey — Tue, 15 Nov 2011 08:26:53 +0000

Brilliant job!!! Thank you

By: edu

edu — Mon, 24 Oct 2011 08:38:26 +0000

show the difference between langrange polynomial and newton interpolating polynomial

By: ankit

ankit — Wed, 12 Oct 2011 13:33:35 +0000

excellent work….helped me alot..

By: Pavel Holoborodko

Pavel Holoborodko — Fri, 05 Aug 2011 00:27:58 +0000

Do you mean quadrature based on “Associated Legendre” polynomials? I don’t know this kind of quadrature.
Could you be more specific – what task do you solve ?

By: vladan

vladan — Thu, 04 Aug 2011 13:12:29 +0000

Do you know where I can find “Abscissae and Weights of Gauss-Legendre Quadrature” for “Associated Legendre”?

By: Gowri Priya

Gowri Priya — Thu, 14 Jul 2011 07:36:39 +0000

Thank u very much for giving useful information