Studies the case where the preconditioner is a Krylov subspace method. Outer iteration; Convergence theory of inner-outer methods.SimonciniValeriaSzyldDanielB.EBSCO_AspSiam Journal on Numerical AnalysisV. Simoncini and D.B. Szyld. Flexible inner-outer Krylov subspace methods. SIAM J. Numer. Anal.,...
Next we introduce the new inner-outer subspace method named FGCRO-DR. A theoretical comparison of both algorithms is then made in the case of flexible preconditioning. It is proved that FGCRO-DR and FGMRES-DR are algebraically equivalent if a collinearity condition is satisfied. While being ...
The output is the estimated dipole moment vector for each point of the source space, and a diagnostics matrix indicating the number of inner iterations for each outer iteration, and the relative change in when tolerance is reached. 4. _ : This function plots the activity map, that is ...
integral equation methodsmethod of mo-mentsmultilevel fast multipole algorithmkrylov subspace methodsThis paper presents flexible inner-outer Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving scattering problems with mixed dielectric and conducting object. The ...
In this paper, flexible inner-outer Krylov subspace methods, which are implemented using the fast multipole method (FMM) for solving large-scale electromagnetic wave problems, are presented. The flexible Krylov subspace methods refer to a class of methods that accept variable preconditioning. To ...
Krylov subspace methodsnon-Hermitian systemspreconditioned conjugate gradientvariable preconditionersA variant of the GMRES algorithm is presented that allows changes in the preconditioning at every step. There are many possible applications of the new algorithm, some of which are briefly discussed...
Krylov Subspace MethodFlexible PreconditioningInner-Outer IterationGPBi-CGWe present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any...
KrylovSubspaceMethodFlexiblePreconditioningInner-OuterIterationGPBi-CGWe present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any iterat...