A Solver for the Rightmost Eigenvalues

Reliable computation of a few eigenvalues of largest real part through exponential transformation

This is a MATLAB software package for reliable computation of a few eigenvalues of largest real part (rightmost) of a large sparse matrix A or a matrix pencil (A,B). It is based on the exponential transformation A --> exp(h*inv(B)*A) (h > 0), which maps the rightmost eigenvalues of A to the dominant (largest in modulus) eigenvalues of exp(h*inv(B)*A). The matrix exponential itself is not formed explicitly; instead, only its action on vectors is needed to invoke MATLAB's eigs. The input matrix (pencil) should have vast majority of eigenvalues of negative real part, and may have a small number of eigenvalues of relatively small positive real part. More details can be found in readme.txt and the main MATLAB file expm_LR_eigs.m