ABSTRACT
Normalized implicit preconditioned conjugate gradient-type schemes based on finite element normalized approximate factorization procedures for solving sparse linear systems, which are derived from the finite element method of partial differential equations in three space variables, are presented. Theoretical estimates on the rate of convergence and computational complexity of the normalized implicit preconditioned conjugate gradient method are also given. The application of the proposed method on a characteristic three-dimensional boundary value problem is discussed and numerical results are given.