The main idea is to transform the constrained 2-1 minimization problem obtained by applying the IRLS method to a 2-2 one that allow regularization matrices in the usual 2-norm regularization term. The regularization parameter that controls the equilibrium between the minimization of the two terms ...
The procedure to determine the stepsize is similar to the adaptive strategy used in many ODE solvers. We assume that the error is approximately Cτq+1, for some constants q,C∈R. The order q is set to q=m4−1 for the first step as in [21] and if a previously suggested stepsize...
It is well known that multigrid solution methods are optimal O(N) solvers, when all components in a method are chosen correctly. For difficult problems, such as some systems of nonlinear equations, it is far from trivial to choose these optimal components. The influence on the multigrid ...
Parallelism and convergence in iterative linear solvers method have been described in the literature, including the generation of Krylov subspace bases with the aid of suitably chosen Chebyshev or Newton ... B Philippe,J Erhel,B Philippe,... 被引量: 0发表: 0年 Fast 3-D simulation of transie...
Iterative solvers based on Krylov subspace method proved to be robust in the presence of well monitored inexact matrix vector products. In this paper, we show that the iterative solver performs well while gradually reducing the number of nonzero elements of the matrix throughout the iterations. ...
Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems Some algorithms based upon a projection process onto the Krylov subspace $K_m = \\operatorname{Span}(r_0, Ar_0, \\ldots, A^{m - 1}r_0)$ are developed, gene... Yousef Saad - 《Mathematics of Computation》 被引量:...
block Krylov subspace methodslow-rank compressionrestartsBlock Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, e.g., from the discretization of partial differential equations. While extended and rational block ...
[11,1,10,2],howeversinceeachstepSylvesterequation,methodcouldexpensivewhendirectsolversused.Othermethodsstructure-preservingdoublingalgorithm(SDA)[12]alternatelylinearizedimplicit(ALI)iterationmethods[13]havebeenproposed.Generally,fixedpointiterationmethods[1,2,14–16]lessexpensivethanSDAmethods.However,slow(linear...
consider that a complex-valuedn×nlinear systemAx=bcan always be rewritten using only real arithmetic as a2n×2nreal-valued system. The primary reason to developLightKrylovis to couple it with high-performance solvers in computational mechanics which often use exclusively real-valued data types. As...
It has been found that all hybrid solvers are superior to the standalone AgMG when a stringent convergence criterion is imposed, but the superiority is weakened with the convergence criterion coarsening. Due to its expensive setup cost, AMG1R5 is not appropriate for the segregated solver.doi:...