Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently, these methods are attractive for solving large-scale nonlinear systems. However, the convergence of these algorithms may be slow in critical cases; therefore, acceleration procedures are welcome. Anderson-like accelerations are widely used in electronic structure calculations to improve a fixed point algorithm for finding Self Consistent Field (SCF) solutions of Hartree-Fock models. In this paper, it is showed how to apply this type of acceleration to Sequential Residual Methods. The performance of the resulting algorithm is illustrated by applying it to the solution of very large problems coming from the discretization of partial differential equations.

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View Secant acceleration of sequential residual methods for solving large-scale nonlinear systems of equations