1,721,031 research outputs found
Block--diagonal and indefinite symmetric preconditioners for mixed finite element formulations
No full textWe are interested in the numerical solution of large structured
indefinite symmetric linear systems arising in mixed finite element
approximations of the magnetostatic problem; in particular, we analyze definite
block--diagonal and indefinite symmetric preconditioners. Relating the
algebraic characteristics of the resulting preconditioned matrix to the
properties of the continuous problem and of its finite element discretization,
we show that the considered preconditioning strategies make the used Krylov
subspace solver insensitive to the mesh refinement parameter, in terms of
number of iterations. In order to achieve computational efficiency, we also
analyze algebraic approximations to the optimal preconditioners, and discuss
their performance on real two and three dimensional application problems
A new investigation of the extended Krylov subspace method for matrix function evaluations
No full textAbstract. For large square matrices A and functions f, the numerical approximation of the action of f(A) to a vector v has received considerable attention in the last two decades. In this paper we investigate the Extended Krylov subspace method, a technique that was recently proposed to approximate f(A)v for A symmetric. We provide a new theoretical analysis of the method, which improves the original result for A symmetric, and gives a new estimate for A nonsymmetric. Numerical experiments confirm that the new error estimates correctly capture the linear asymptotic convergence rate of the approximation. By using recent algorithmic improvements, we also show that the method is computationally competitive with respect to other enhancement techniques
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