Residual Smoothing Techniques for Iterative Methods

VML : A Class of Virtual Multi - Level Iterative

We introduce virtual multi-level iterative methods (VML) which attempt to remove the low frequency errors by conducting some special smoothing (residual norm minimization) procedure with respect to the coarse grids. However, there is no coarse grid formed explicitly, no inter-grid transfer operator is needed, and even the smoothing procedure can be done almost locally. These properties are attr...

Minimal Residual Smoothing in Multi-Level Iterative Method

A minimal residual smoothing (MRS) technique is employed to accelerate the convergence of the multi-level iterative method by smoothing the residuals of the original iterative sequence. The sequence with smoothed residuals is reintroduced into the multi-level iterative process. The new sequence generated by this acceleration procedure converges much faster than both the sequence generated by th...

Residual Smoothing Techniques: Do They Improve the Limiting Accuracy of Iterative Solvers?

Residual Smoothing and Peak/plateau Behavior in Krylov Subspace Methods

Recent results on residual smoothing are reviewed, and it is observed that certain of these are equivalent to results obtained by different means that relate “peaks” and “plateaus” in residual norm sequences produced by certain pairs of Krylov subspace methods.

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...