A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations

We present an iterative method for solving large sparse nonsymmetric linear systems of equations that enhances Manteuflel’s adaptive Chebyshev method with a conjugate gradient-like method. The new method replaces the modified power method for computing needed eigenvalue estimates with Arnoldi’s method, which can be used to simultaneously compute eigenvalues and to improve the approximate solution. Convergence analysis and numerical experiments suggest that the method is more efficient than the original adaptive Chebyshev algorithm.