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how to solve the maximum eigenvalue of a matrix

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tarkyss

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i hope the algorithm suits for vlsi implementation
 

Hi tarkyss
There is an itrative method for calculation of maximum aigenvalue of a matrix by name of Method of Power that I think it is easy to implement.
I saw it in the book "Numerical Methods in Electromagnetics" by Sadiko.
Now time is late, if you cannot find any information about this method notify me.

Regards.
 

the itrative counter are constant?
if not, i think it may be not for suit for hardware implemented, because the time cannot be controlled,
i searched many algorithms, for example QL algorithm JACOBA algorithm exponent multiplier, but all algorithms have the same question, maybe there are some hadware method to solve this question, but i dont know
 

hi tarkyss
1- In this method you can only calculate the biggest eigenvalue.
2- Like other iterative algorithms, more iteration lead in better and more exact results.
regards
 

mahdithdn
Do you mean that if i only want to calculate the biggest eigenvalue, the itrative counter is fixed?
if so, which algorithms can do that?

Added after 2 hours 33 minutes:

another question, can householder and QL algorithm process complex matrix?
if not? how to solve the eigenvalue and eigenvector of a complex matrix?
 

use newton method to get every eigenvalues, and sorting.
The iteration count ..... it depends on the precision you want and initial value. I think to try it is the best policy
 

but if we want to restrict the iteration count,
for example, the iteration cannot more than 10 times. newton method cannot tell me the precision for any matrix, so i dont think it is a good method for vlsi implemention
 

Hi tarkyss
I've attached for you some part of "Numerical Methods in Electromagnetics" by Sadiko.
it explaine both Power Method & Jacobi Method.
as dinolin said number of iteration depends on desired precision. but maybe some methods converge better to the answer.
I think the Power Method has no matter with complex problem.
Best. mah
 

thanks, but for vlsi implemention, if the maximum iteration number is 10, can you tell me the precision for any matrix? of course the iteration depends on desired presion, but it depends on data too.
 

Dear friend:
Could you please attach the book "Numerical Methods in Electromagnetics" by Sadiko.
regards
 

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