How to solve this kind of eigenvalue problem?

  • Thread starter jollage
  • Start date
  • #1
63
0
I know that eigenvalue problem like [itex]Lq=\lambda q[/itex] could be easily solved by eig command in Matlab.

But how to solve a problem like [itex]Lq=\lambda q + a[/itex], where [itex]a[/itex] has the same dimension with the eigenfunction [itex]q[/itex]?

Thanks a lot in advance.

Jo
 
Last edited by a moderator:

Answers and Replies

  • #2
63
0
OK, by reading the article On Inhomogeneous Eigenvalue Problems by Mattheij and Soderlind, this kind of the eigenvalue problem could be solved.

Then I have a new problem, which is [itex]Lq=\lambda q + b\lambda^2[/itex], where b has the same dimension with q. Note that now [itex]\lambda[/itex] is squared and unknown.

How to solve this problem? Thank you.

Jo
 
Last edited:
  • #3
35,135
6,884
Doesn't the article you cited give any insight? It seems odd to me that the authors would trade one problem (solving for eigenvalues in Lq = λq + a) for what seems to be a harder problem, without providing some direction.
 
  • #4
63
0
Doesn't the article you cited give any insight? It seems odd to me that the authors would trade one problem (solving for eigenvalues in Lq = λq + a) for what seems to be a harder problem, without providing some direction.

Dear Mark,

Thank you. My apologies. I only read half of that paper, till where I have found the way to attack the problem Lq = λq + a directly. The remaining part of the paper introduces a method called power iteration.

I thought this kind of problem could be easily and directly solved with some tricks that I still do not know. (like the quadratic eigenvalue problem to be solved with a new eigenfunction, which is elegant and smart). I have a feeling that problem like these two I posted here could always be solved using some iteration methods by guessing and adjusting then guessing... I want to know the elegant and smart way, the so-called tricks.

The second problem is more complex since now λ is squared in the third term while the first problem has only a constant additional term.

Maybe I should finish that paper. Otherwise if you have some experiences and tricks, please share. Thank you.

Jo
 
Last edited:

Related Threads on How to solve this kind of eigenvalue problem?

Replies
1
Views
638
Replies
6
Views
6K
Replies
13
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
2
Replies
34
Views
5K
  • Last Post
Replies
5
Views
11K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
3
Views
1K
Top