Efficient iterative solution of linear systems from discretizing singular integral equations.
Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods
We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a...
Efficient preconditioning for sequences of parametric complex symmetric linear systems.
Efficient solution of symmetric eigenvalue problems using multigrid preconditioners in the locally optimal block conjugate gradient method.
Ein effizienter Algorithmus zur iterativen Einschliessung der inversen Matrix
Es wird ein kombinierter Algorithmus zur iterativen Einschlissung der Inversen einer Matrix beschrieben. Es handelt sich dabei um eine intervallmässige Version des Schulz'schen Verfahrens. Es wird bewiesen, dass der Algorithmus genauso effizient ist wie ein hisher bekannter aus [2], dass er aber in Bezug auf den akkumulierten Rundungsfehler dem bisherigen Vorgehen vorzuziehen ist. Ein numerisches Beispiel wird gegeben.
Eine Bemerkung über Iterationsverfahren.
Einige Bemerkungen zur numerischen Stabilität von Matrizeniterationen
Enhancement of Krylov subspace spectral methods by block Lanczos iteration.
Epsilon-inflation with contractive interval functions
For contractive interval functions we show that results from the iterative process after finitely many iterations if one uses the epsilon-inflated vector as input for instead of the original output vector . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.
Erratum. Factorization Iterative Methods, M-operators and H-Operators. (Num. Math. 31, 335-357 (1979)).
Erratum. On the Multi-Level Splitting of Finite Element Spaces.(Numer. Math. 49, 379-412 (1986)).
Error estimation on the Padé approximation of transfer functions via the Lanczos process.
Estimates for Multigrid Methods Based on Red-Black Gauss-Seidel Smoothings.
Euclid΄s algorithm and accelerated iterative methods
Evaluation of the condition number in linear systems arising in finite element approximations
This paper derives upper and lower bounds for the -condition number of the stiffness matrix resulting from the finite element approximation of a linear, abstract model problem. Sharp estimates in terms of the meshsize h are obtained. The theoretical results are applied to finite element approximations of elliptic PDE's in variational and in mixed form, and to first-order PDE's approximated using the Galerkin–Least Squares technique or by means of a non-standard Galerkin technique in L1(Ω). Numerical...
Experiments with Krylov subspace methods on a massively parallel computer
In this note, we compare some Krylov subspace iterative methods on the MASPAR, a massively parallel computer with 16K processors. In particular, we apply these methods to solve large sparse nonsymmetric linear systems arising from elliptic partial differential equations. The methods under consideration include conjugate gradient type methods, semiiterative methods, and a hybrid variant. Our numerical results show that, on the MASPAR, one should compare iterative methods rather on the basis of total...
Explicit conjugate gradient method with preconditioning
An algorithm of the preconditioned conjugate gradient method in which the solution of an auxiliary system is replaced with multiplication by the matrix for suitably chosen is presented.
Extrapolated Gauss-Seidel I and SOR Methods for Least-Squares Problems.
Extrapolated positive definite and positive semi-definite splitting methods for solving non-Hermitian positive definite linear systems
Recently, Na Huang and Changfeng Ma in (2016) proposed two kinds of typical practical choices of the PPS method. In this paper, we extrapolate two versions of the PPS iterative method, and we introduce the extrapolated Hermitian and skew-Hermitian positive definite and positive semi-definite splitting (EHPPS) iterative method and extrapolated triangular positive definite and positive semi-definite splitting (ETPPS) iterative method. We also investigate convergence analysis and consistency of the...
Extrapolation of S. O. R. iterations