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How to numerically calculate the complex roots (eigenvalues) of a determinant?

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Please consider the following determinant:
"aij" and "bij" take on values lager than zero and smaller than one, and "q" has a range between pi and -pi. I want to calculate the complex eigenvalues (lambda) of the determinant using some sort of a numerical scheme.
I'm well aware that Computer Algebra Systems like MATLAB have no problem calculating the roots of a determinant of this size, but I am working with matrices that are ridiculously larger than this one and without an efficient numerical solution, they would take forever to get solved.
I would immensely appreciate any help or insight.
Thank you very much
Walter Roberson
Walter Roberson on 12 Jun 2022
To be honest, I do not have enough enthusiasm to bother typing in those equations by hand starting from an image.
If you had used syms lambda and posted the code to construct the matrix, then I would have been more likely to take a look.

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Answers (1)

Sergio Yanez-Pagans
Sergio Yanez-Pagans on 11 Jun 2022

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