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- Using the QZ eigenvalue solver

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utab

Beginner

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03-21-2012
01:53 AM

111 Views

Using the QZ eigenvalue solver

I have a system like

K1 K12

0 K2

and

M1 0

M21 M2

where M21= - K12^T

If I use this model to solve the eigenvalue problem with the qz solver, I get the independent eigenvalues of the blocks, namely, the eigenvalues of (K1,M1) and (K2,M2)? The coupling blocks seem to be not taken into consideration. What could be the cause of this?

What should be the path to use the QZ nonsymmetric eigenvalue solver?

Following the documentation, I guess I should do,

+ balance to improve for performance: ggbal

+ then reduced to hessenberg format: gghrd

+ use the solver: hgeqz

+ recover: ggbak

Is this correct?

If this is correct, then there is a problem because the problem gives me eigenvalues of the blocks only as explained.

Best,

Umut

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3 Replies

Victor_K_Intel1

Employee

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03-22-2012
03:53 AM

111 Views

Usually it is much easier to help if the test is provided.

From the first glance, the sequence of calls you refer to looks OK.

But at the same time, describing the matrices you draw them as block upper triangular and block lower triangular. But for the QZ solver one of matrices should be in the upper Hessenberg form, the second - in the upper triangular form. This might be the root cause of the issue you observe.

WBR

Victor

utab

Beginner

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03-26-2012
02:41 AM

111 Views

Does not the routine of reduction to hessenberg format, namely the second line in my input, do that for me so that the input matrices are in right format?

Best,

Umut

Victor_K_Intel1

Employee

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03-26-2012
04:18 AM

111 Views

Actually it does but assuming the second matrix is already in the form of upper triangular matrix.

Unfortunately, from your description it is not obvious.

WBR

Victor

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