Coding Eigen Solver in Matlab: Jacobi/Lanczos vs Vector Iteration

In summary, when coding an Eigen solver in Matlab for a research project, you may encounter complex eigenvalues. The Vector iteration method can be used, but it requires a dominant eigenvalue and may not always work. For more robust solutions, consider using Jacobi/Lanczos solvers, which can calculate all eigenvalues but may take longer to converge.
  • #1
svishal03
129
1
I'm to code the Eigen solver in Matlab for a reserach project.

The project concerned might also give me complex eigen values.

I have been formulating the algorithm for Vector iteration method (or otherwise called the Power method) for the computation of eigen values/eigen vectors.

The method fails when there is no dominant eigen value.

Please can anyone suggest about the method to be used for coding Eigen solver?

Can vector iteeration solve for complex eigen values?

Can vector ietartion calculate all eigen values?

Please can anyone comment on JAcobi/Lanczos solver pleasE?
 
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  • #2
Vector iteration can solve for complex eigenvalue, however it requires a dominant eigenvalue to work. Jacobi/Lanczos solvers are more robust than the vector iteration method, and can calculate all eigenvalues. These are iterative methods, which means they can take longer to converge. However, if you need to calculate all eigenvalues, they may be your best option.
 

1. What is the purpose of coding an eigen solver in Matlab?

The purpose of coding an eigen solver in Matlab is to find the eigenvalues and eigenvectors of a given matrix. Eigenvalues and eigenvectors are important in many scientific and engineering applications, such as in solving differential equations, analyzing systems of linear equations, and understanding the behavior of dynamical systems.

2. What is the difference between Jacobi/Lanczos and Vector Iteration methods?

Jacobi/Lanczos and Vector Iteration methods are both iterative methods used to find eigenvalues and eigenvectors. The main difference between the two is their convergence rate. Jacobi/Lanczos method converges faster than Vector Iteration, but it requires more computation. Vector Iteration, on the other hand, is simpler to implement but may take more iterations to reach the desired accuracy.

3. How do I determine which method to use for my problem?

The choice of method depends on the specific characteristics of the problem at hand. Jacobi/Lanczos method is more suitable for large matrices with a high number of eigenvalues, while Vector Iteration is better suited for smaller matrices with a few dominant eigenvalues. It is recommended to test both methods and compare their performance to determine which one is more efficient for your specific problem.

4. Are there any limitations to coding an eigen solver in Matlab?

Yes, there are certain limitations to consider when coding an eigen solver in Matlab. The accuracy of the eigenvalues and eigenvectors depends on the machine precision of the computer and the stability of the algorithm. Additionally, for very large matrices, the computation time and memory usage can become significant.

5. How do I validate the results obtained from the eigen solver?

To validate the results obtained from the eigen solver, you can use the fact that the eigenvalues and eigenvectors satisfy the eigenvalue equation Ax = λx, where A is the original matrix, λ is the eigenvalue, and x is the corresponding eigenvector. You can also compare the results with other methods or known analytical solutions for the specific problem.

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