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Nearly optimal convergence result for multigrid with aggressive coarsening and polynomial smoothing

Petr Vaněk, Marian Brezina (2013)

Applications of Mathematics

We analyze a general multigrid method with aggressive coarsening and polynomial smoothing. We use a special polynomial smoother that originates in the context of the smoothed aggregation method. Assuming the degree of the smoothing polynomial is, on each level k , at least C h k + 1 / h k , we prove a convergence result independent of h k + 1 / h k . The suggested smoother is cheaper than the overlapping Schwarz method that allows to prove the same result. Moreover, unlike in the case of the overlapping Schwarz method, analysis...

New iterative codes for𝓗-tensors and an application

Feng Wang, Deshu Sun (2016)

Open Mathematics

New iterative codes for identifying 𝓗 -tensor are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor, i.e., an even-degree homogeneous polynomial form are given. Advantages of results obtained are illustrated by numerical examples.

New mixed finite volume methods for second order eliptic problems

Kwang Y. Kim (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local discontinuous Galerkin method. We propose two different types of methods, called Methods I and II, and show that they have distinct advantages over...

New SOR-like methods for solving the Sylvester equation

Jakub Kierzkowski (2015)

Open Mathematics

We present new iterative methods for solving the Sylvester equation belonging to the class of SOR-like methods, based on the SOR (Successive Over-Relaxation) method for solving linear systems. We discuss convergence characteristics of the methods. Numerical experimentation results are included, illustrating the theoretical results and some other noteworthy properties of the Methods.

Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

Jim Douglas Jr., Juan E. Santos, Dongwoo Sheen, Xiu Ye (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H1(Ω)...

Nonmonotone strategy for minimization of quadratics with simple constraints

M. A. Diniz-Ehrhardt, Zdeněk Dostál, M. A. Gomes-Ruggiero, J. M. Martínez, Sandra Augusta Santos (2001)

Applications of Mathematics

An algorithm for quadratic minimization with simple bounds is introduced, combining, as many well-known methods do, active set strategies and projection steps. The novelty is that here the criterion for acceptance of a projected trial point is weaker than the usual ones, which are based on monotone decrease of the objective function. It is proved that convergence follows as in the monotone case. Numerical experiments with bound-constrained quadratic problems from CUTE collection show that the modified...

Nonrecursive solution for the discrete algebraic Riccati equation and X + A*X -1 A=L

Maria Adam, Nicholas Assimakis (2015)

Open Mathematics

In this paper, we present two new algebraic algorithms for the solution of the discrete algebraic Riccati equation. The first algorithm requires the nonsingularity of the transition matrix and is based on the solution of a standard eigenvalue problem for a new symplectic matrix; the proposed algorithm computes the extreme solutions of the discrete algebraic Riccati equation. The second algorithm solves the Riccati equation without the assumption of the nonsingularity of the transition matrix; the...

Nonsingularity and P -matrices.

Jiří Rohn (1990)

Aplikace matematiky

New proofs of two previously published theorems relating nonsingularity of interval matrices to P -matrices are given.

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