Self consistent method for eigenvalues

In summary, there are various techniques available to improve the convergence of SCF calculations, with the most commonly used being DIIS and its variations. This could be a useful starting point for improving the convergence of the nonlinear Schrodinger equation and finding its eigenvalues.
  • #1
babylonia
11
0
Hi all,

I am trying to find numerically the eigenvalues of a nonlinear schroedinger equation in a similar way as the Self Consistent Field method for Hatree-Fock problems. Does anybody know in the SCF calculation how to improve the convergency? Is there any trick other than simply inserting the solution back for the next iteration?

Any clues would be appreciated. Thank you.
 
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  • #2
There are a number of techniques to stabilize and improve SCF convergence. The one that's most used by far is http://en.wikipedia.org/wiki/DIIS" (and variants of it) though. So that's probably a good place to start.
 
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FAQ: Self consistent method for eigenvalues

1. What is a self consistent method for eigenvalues?

A self consistent method for eigenvalues is a numerical technique used to calculate the eigenvalues (or characteristic values) of a matrix. It involves repeatedly solving a system of equations until the values converge to a stable solution.

2. How does a self consistent method for eigenvalues work?

This method works by starting with an initial guess for the eigenvalues and then using an iterative process to adjust the values until they converge to a stable solution. This is typically done using algorithms such as the power method or the Jacobi method.

3. What are the advantages of using a self consistent method for eigenvalues?

One advantage is that it can be used to calculate eigenvalues for large matrices, which may not be possible using other methods. It is also relatively fast and efficient compared to other numerical techniques for finding eigenvalues.

4. Are there any limitations to using a self consistent method for eigenvalues?

Yes, this method may not always converge to the correct solution, especially if the initial guess is not close enough to the true eigenvalues. It also may not work well for matrices with complex or repeated eigenvalues.

5. How is a self consistent method for eigenvalues used in scientific research?

This method is commonly used in various fields of science, such as physics, chemistry, and engineering, to solve problems and analyze data involving matrices with eigenvalues. It is especially useful for studying quantum systems and electronic structures in materials.

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