Factored Inverses of Real Symmetric Matrices
Jane K. Cullum, Ralph A. Willoughby · Birkhäuser Boston eBooks · 1985
The FORTRAN codes in this chapter address the question of computing distinct eigenvalues and corresponding eigenvectors of a real symmetric matrix by applying a single-vector Lanczos procedure to the inverse of an associated matrix B ≡ PCPT, where C = S0*A + SHIFT*I. The scalars S0 and SHIFT are specified by the user, selected in such a way that the resulting matrix C (or B) has a reasonable numerical condition. The permutation matrix P is chosen so that for a sparse matrix A, the resulting factorization of B is also sparse.