Error Estimators for a Krylov Subspace Iterative Method for Solving Linear Systems of Equations with a Symmetric Indefinite Matrix

This paper describes a Krylov subspace iterative method designed for solving linear systems of equations with a large, symmetric, nonsingular, and indefinite matrix. This method is tailored to enable the evaluation of error estimates for the computed iterates. The availability of error estimates makes it possible to terminate the iterative process when the estimated error is smaller than a user-specified tolerance. The error estimates are calculated by leveraging the relationship between the iterates and Gauss-type quadrature rules. Computed examples illustrate the performance of the iterative method and the error estimates.