MATLAB: Sensitivity study of eigenvalues

Question

Hi All,

There is a matrix (14×14), and some of its elements are functions of a variable. I want to study the sensitivity of the matrix eigenvalues when varying the variable.

First, I need to figure out the transitions of individual eigenvalues along the variable. But I have the following issue. For example, two set of eigenvalues [s11, s21, s31, s41, … ] and [s12, s22, s32, s42, … ] for variable x=x1 and x=x2, respectively, are obtained by simply using eig Matlab command. As I know, the generated eigenvalues have no particular order, which means s12 is not necessarily the transition of s11. The questions is how I find the transition of an individual eigenvalue such as s11 when the variable changing from x1 to x2, x3, …?

I know that by plotting all eigenvalues on a single figure (similar to root locus plot), we can OBSERVE the transitions. But I want to a way to automatically record the transition. Any help is welcome. Many thanks.

Answer 1

I wrote a code called eigenshuffle some years ago, that would take a sequence of eigenvector/value problems, and try to shuffle the order returned to resolve these problems. It is still on the file exchange.