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Both of them are solving the same problem, eigenvalues and eigenvectors of a general matrix
I want to ask, in terms of computational time, which one is faster ??
also, in terms of performance, which one is better?
If I don't want to balance or permute my matrix(BALANC = 'N' in dgeevx ), then is dgeevx the same as dgeev ??
I am solving a second order linear ODE, which one should I use? dgeev or dgeevx ?
Thank you very much
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Both dgeevx and dgeev compute eigenvalues and, optionally, eigenvectors. Both routines use the same underlying computational routines to achieve this so you should not see any difference in efficiency. But dgeevx can also compute condition numbers for you which can be very helpful in giving you information about the sensitivity of your problem. See Section 4.8 of the Users' Guide (Error Bounds for the Nonsymmetric Eigenproblem) for further details.
The down side of computing the eigenvector condition numbers is that additional n by n workspace is required, which only really matters if your matrices are very large.
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