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On the parameter in augmented Lagrangian preconditioning for isogeometric discretizations of the Navier-Stokes equations

Jiří Egermaier, Hana Horníková (2022)

Applications of Mathematics

In this paper, we deal with the optimal choice of the parameter γ for augmented Lagrangian preconditioning of GMRES method for efficient solution of linear systems obtained from discretization of the incompressible Navier-Stokes equations. We consider discretization of the equations using the B-spline based isogeometric analysis approach. We are interested in the dependence of the convergence on the parameter γ for various problem parameters (Reynolds number, mesh refinement) and especially for...

On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements

Michal Křížek, Jaroslav Mlýnek (1994)

Banach Center Publications

The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.

On the reduction of a random basis

Ali Akhavi, Jean-François Marckert, Alain Rouault (2009)

ESAIM: Probability and Statistics

For p ≤ n, let b1(n),...,bp(n) be independent random vectors in n with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If b ^ 1 ( n ) , ... , b ^ p ( n ) is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...

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