For a diagonal matrix with diagonal elements equal to eigen values, I am interested to further use this matrix to carry out transient analysis using a numerical method (trapezoidal rule). There are large number (thousands) of very similar (almost same) eigen values in this matrix but I can't take them all due to computational complexity and very long run time required for transient analysis for such a high dimensional matrix. Taking only a few most significant eigen values (corresponding to the most dominant poles) make the results very inaccurate and hence doesn't serve the purpose.
Need some guidance if there's a way to deal with this accuracy vs long run time issue? In short if there's some way to compactly represent the matrix having thousands of duplicate eigen values & use the compact Matrix for transient analysis.
