Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization
David Sanborn Scott · SIAM Journal on Numerical Analysis · 1981
In this paper we discuss an iterative technique for finding the algebraically smallest (or largest) eigenvalue of the generalized eigenvalue problem $A - \lambda M$, where A and M are real, symmetric, and M is positive definite. We assume that A and M are such that it is undesirable to factor the matrix $A - \sigma M$ for any value of $\sigma $. We prove that the algorithm is globally convergent, and that convergence is asymptotically quadratic. Finally, we discuss the modifications required in the algorithm to make it computationally feasible.