Generalised eigen system - Extracting eigen values and eigen vectors from given matrices

Hi,

I am working on parametric model fitting (ellipse fitting) using direct least squares method. I have two matrices namely, a design scatter matrix A and a constraint matrix B with which I need to find the Ellipse parameters. I am aware that matlab function 'eig' gives me the results in terms of eigen values and eigen vectors which can be further processed to actual results.

I am keen to learn the way in which matlab function 'eig' works mathematically. Any links to relevant sources will be helpful too. I like to learn the actual mathematical approach in eig function design as I shall have to code this methodology into managed C++.

Please share your knowledge on how to re-write 'eig' function.

Regards,

Bhaskar

Answer 1

[Andrew Newell]

It would be a waste of time to write your own code for this when there are robust packages available for free. See Template Numerical Toolkit.

However, if you want to understand the numerical methods for finding eigenvalues, I would recommend Golub, Gene H.; Van Loan, Charles F. (1996), Matrix Computations.