Inexact Newton Method For Solving Large Symmetric Sparse Eigenvalue Problems

Inexact Newton method is an effective method for computing the extremeeigenvalues of symmetric matrices. In this paper we emphasize on studying theconvergence of inexact Newton method. We make use of the theories of the inexact Newton method for solving nonlinearequations and study the convergence of the inexact Newton method for solvingeigenvalue problems. The main result is that under certain conditions the inexactNewton method for eigenvalue problems is superlinear convergent. The convergencetheories of preconditioned inexact Newton method and preconditioned block inexactNewton method are also analyzed. An inexact Newton method for solving generalizedeigenvalue problems is also proposed in this paper. All kinds of methods are compared in the numerical experiments. The numericalresults show that the inexact Newton method is effective and the analyses in thispaper are correct.