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1
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On the two-step iterative method of solving frictional contact problems in elasticity

100%
Angelov T., Liolios A.
International Journal of Applied Mathematics and Computer Science
|
2005
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tom 15
|
nr 2
197-203
EN
A class of contact problems with friction in elastostatics is considered. Under a certain restriction on the friction coefficient, the convergence of the two-step iterative method proposed by P.D. Panagiotopoulos is proved. Its applicability is discussed and compared with two other iterative methods, and the computed results are presented.
2
Content available remote

Algebraic approach to domain decomposition

80%
Práger M.
Banach Center Publications
|
1994
|
tom 29
|
nr 1
207-214
EN
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.
3
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Acceleration properties of the hybrid procedure for solving linear systems

80%
Abkowicz A., Brezinski C.
Applicationes Mathematicae
|
1995-1996
|
tom 23
|
nr 4
417-432
EN
The aim of this paper is to discuss the acceleration properties of the hybrid procedure for solving a system of linear equations. These properties are studied in a general case and in two particular cases which are illustrated by numerical examples.
4
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Computation of double Hopf points for delay differential equations

80%
Xu Y., Shi T.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
Relating to the crucial problem of branch switching, the calculation of codimension 2 bifurcation points is one of the major issues in numerical bifurcation analysis. In this paper, we focus on the double Hopf points for delay differential equations and analyze in detail the corresponding eigenspace, which enable us to obtain the finite dimensional defining system of equations of such points, instead of an infinite dimensional one that happens naturally for delay systems. We show that the double Hopf point, together with the corresponding eigenvalues, eigenvectors and the critical values of the bifurcation parameters, is a regular solution of the finite dimensional defining system of equations, and thus can be obtained numerically through applying the classical iterative methods. We show our theoretical findings by a numerical example.
5
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Inequality-based approximation of matrix eigenvectors

70%
Kocsor A., Dombi J., Bálint I.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
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nr 4
533-538
EN
A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.
6
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Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids

61%
Collignon T., Van Gijzen M.
International Journal of Applied Mathematics and Computer Science
|
2010
|
tom 20
|
nr 1
109-121
EN
Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.
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