If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these eigenvalues? I guess with the information about eigenvalues, there should be some quicker way to compute eigenvectors of the matrix compared with simply diagonalize it without any information.
Compute eigenvectors of a matrix with known eigenvalue spectrum
algorithms;eigenvalues;matrix;numerical