Several problems in early vision have been formulated in the past in a regularization framework. These problems, when discretized, lead to large sparse linear systems. In this paper, we present a novel physically based adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to dramatically improve the speed of convergence for solving the aforement...

Incomplete LDL factorizations sometimes produce an indefinite preconditioner evenwhen the input matrix is Hermitian positive definite. The two most popular iterative solvers for symmetric systems, CG and MINRES, cannot use such preconditioners; they require a positive definite preconditioner. One approach, that has been extensively studied to address this problem is to force positive definitene...

We study the performance of a new block preconditioner for class \(3\times 3\) saddle point problems which arise from finite-element methods solving time-dependent Maxwell equations and some other practical problems. also estimate lower upper bounds eigenvalues preconditioned matrix. Finally, we examine our to accelerate convergence speed GMRES method shows effectiveness preconditioner.

Lower bounds for the condition numbers of the preconditioned systems are obtained for the Bramble-Pasciak-Schatz substructuring preconditioner and the Neumann-Neumann preconditioner in two dimensions. They show that the known upper bounds are sharp.

We introduce a method for constructing an element-by-element sparse approximate inverse (SAI) preconditioner designed to be effective in a massively-parallel spectral element modeling environment involving nonsymmetric systems. This new preconditioning approach is based on a spectral optimization of a low-resolution preconditioned system matrix (PSM). We show that the local preconditioning matr...

We study the preconditioned iterative method for the unsteady Navier-Stokes equations. The rotation form of the Oseen system is considered. We apply an efficient preconditioner which is derived from the Hermitian/Skew-Hermitian preconditioner to the Krylov subspace-iterative method. Numerical experiments show the robustness of the preconditioned iterative methods with respect to the mesh size, ...

A convergence theory is presented for a substructuring preconditioner based on constrained energy minimization concepts. The preconditioner is formulated as an Additive Schwarz method and analyzed by building on existing results for Balancing Domain Decomposition. The main result is a bound on the condition number based on inequalities involving the matrices of the preconditioner. Estimates of ...

By combining element-by-element estimates for the field of values of a preconditioned matrix with GMRES-convergence estimates it is possible to derive an easily computable upper bound on the GMRES-residual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The resulting upper bound for the GMRES-residual norm can...

In this paper, the efficiency of a parallelizable preconditioner for Domain Decomposition Methods in the context of the solution of non-symmetric linear equations arising from the discretization of the conservation laws in hydrology (e.g., the coupled surface and sub-surface flow over a freatic acuifer) is investigated. The Interface Strip Preconditioner (IS) proposed is based on solving a prob...

Immersed finite element methods generally suffer from conditioning problems when cut elements intersect the physical domain only on a small fraction of their volume. De Prenter et al. [Computer Methods in Applied Mechanics and Engineering, 316 (2017) pp. 297–327] present an analysis for symmetric positive definite (SPD) immersed problems, and for this class of problems an algebraic precondition...