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MathGroup Archive 1995

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Re: FindMinimum and NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg2745] Re: FindMinimum and NIntegrate
  • From: saarinen (Sirpa Saarinen)
  • Date: Mon, 11 Dec 1995 22:04:41 -0500
  • Organization: Wolfram Research, Inc.

CHAN MUN CHOONG <sci20312 at cobra.nus.sg> writes:

>  This is my first time using Mathematica and I have read the book 
>"Mathematica : A System for Doing Mathematics by Computer"  written by 
>Stephen Wolfram.
>  I find the examples for each function in the book simple and straight 
>forward. If I want to know what the package can really do, which book 
>should be recommended?
>  Is it possible to use Mathematica to calculate the eigenvalues of a 
>Hamiltonian following a variational approach on a trial wave function 
>with a square well.
>  I am trying to use FindMinimum to numerically minimize the the 
>eigenvalues with respect to three parameters; alpha, beta, and gamma.
>  But the problem is that I do not know what optimization method is 
>FindMinimum based on. I have read the book and found no mention of the 
>method used. I also have integration inside the equation. Can FindMinimum 
>handle it?

FindMinimum uses Brent's method for optimization. If your integral can
be done symbolically, you should use Integrate, else you should use
NIntegrate inside FindMinimum, since FindMinimum cannot handle symbolic
information.

>  What method is NIntegrate based on? Do I use Integrate or NIntegrate 
>inside fuction FindMinimum?

For a one-dimensional integral, NIntegrate uses Gauss-Kronrod points
for integration.

>  Can someone please help to clarify. Thanks.

Sirpa Saarinen
saarinen at wri.com





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