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Aggregation/disaggregation method for safety models

Štěpán Klapka, Petr Mayer (2002)

Applications of Mathematics

The paper concerns the possibilities for mathematical modelling of safety related systems (equipment oriented on safety). Some mathematical models have been required by the present European Standards for the railway transport. We are interested in the possibility of using Markov’s models to meet these Standards. In the text an example of using that method in the interlocking equipment life cycle is given. An efficient aggregation/disaggregation method for computing some characteristics of Markov...

Algebraic approach to domain decomposition

Milan Práger (1994)

Banach Center Publications

An iterative procedure containing two parameters for solving linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numerical example is given as an illustration.

Algebraic domain decomposition solver for linear elasticity

Aleš Janka (1999)

Applications of Mathematics

We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.

All-at-once preconditioning in PDE-constrained optimization

Tyrone Rees, Martin Stoll, Andy Wathen (2010)

Kybernetika

The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...

Altman's methods revisited

C. Roland, B. Beckermann, C. Brezinski (2004)

Applicationes Mathematicae

We discuss two different methods of Altman for solving systems of linear equations. These methods can be considered as Krylov subspace type methods for solving a projected counterpart of the original system. We discuss the link to classical Krylov subspace methods, and give some theoretical and numerical results on their convergence behavior.

An adaptive s -step conjugate gradient algorithm with dynamic basis updating

Erin Claire Carson (2020)

Applications of Mathematics

The adaptive s -step CG algorithm is a solver for sparse symmetric positive definite linear systems designed to reduce the synchronization cost per iteration while still achieving a user-specified accuracy requirement. In this work, we improve the adaptive s -step conjugate gradient algorithm by the use of iteratively updated estimates of the largest and smallest Ritz values, which give approximations of the largest and smallest eigenvalues of A , using a technique due to G. Meurant and P. Tichý (2018)....

An alternating-direction iteration method for Helmholtz problems

Jim Douglas, Jeffrey L. Hensley, Jean Elizabeth Roberts (1993)

Applications of Mathematics

An alternating-direction iterative procedure is described for a class of Helmholz-like problems. An algorithm for the selection of the iteration parameters is derived; the parameters are complex with some having positive real part and some negative, reflecting the noncoercivity and nonsymmetry of the finite element or finite difference matrix. Examples are presented, with an applications to wave propagation.

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