Rank-one modification of the symmetric eigenproblem

Summary An algorithm is presented for computing the eigensystem of the rank-one modification of a symmetric matrix with known eigensystem. The explicit computation of the updated eigenvectors and the treatment of multiple eigenvalues are discussed. The sensitivity of the computed eigenvectors to errors in the updated eigenvalues is shown by a perturbation analysis.Support for this research was provided by NSF grants MCS 75-06510 and MCS 76-03139Support for this research was provided by the Applied Mathematics Division, Argonne National Laboratory, Argonne, IL 60439, USA