How residual bounds for restarted GMRES describe the real behaviour

Abstract

Given a system of linear equations Ax = b with a nonsingular matrix A, new three upper bounds for the norm of the residual vector of the restarted GMRES(m) method are presented. The question, 'how accurately these bounds describe the real course of the norm of the residual' is discussed.

The numerical results with graphs compare theoretical and real course.

Keywords

• residual
• bounds
• restarted
• GMRES
• describe
• behaviour