Search results for "Linear subspace"
showing 10 items of 65 documents
Building blocks for odd–even multigrid with applications to reduced systems
2001
Abstract Building blocks yielding an efficient implementation of the odd–even multigrid method for the Poisson problem in the reference domain (0,1) d , d=2,3, are described. Modifications needed to transform these techniques to solve reduced linear systems representing boundary value problems in arbitrary domains are given. A new way to define enriched coarser subspaces in the multilevel realization is proposed. Numerical examples demonstrating the efficiency of developed multigrid methods are included.
Approximation of the Feasible Parameter Set in worst-case identification of Hammerstein models
2005
The estimation of the Feasible Parameter Set (FPS) for Hammerstein models in a worst-case setting is considered. A bounding procedure is determined both for polytopic and ellipsoidic uncertainties. It consists in the projection of the FPS of the extended parameter vector onto suitable subspaces and in the solution of convex optimization problems which provide Uncertainties Intervals of the model parameters. The bounds obtained are tighter than in the previous approaches. hes.
Numerical Approximation of Elliptic Variational Problems
2003
This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.
New applications of extremely regular function spaces
2017
Let $L$ be an infinite locally compact Hausdorff topological space. We show that extremely regular subspaces of $C_0(L)$ have very strong diameter $2$ properties and, for every real number $\varepsilon$ with $0<\varepsilon<1$, contain an $\varepsilon$-isometric copy of $c_0$. If $L$ does not contain isolated points they even have the Daugavet property, and thus contain an asymptotically isometric copy of $\ell_1$.
Spatial weighted averaging for ERP denoising in EEG data
2010
In the present paper we intend to improve the practical accuracy of ERP denoising methods proposed in earlier research by allowing them to take into account possible violations of the underlying assumptions, which often take place in practice. Here we consider ERP denoising approaches operating within the framework of the linear instantaneous mixing model that consist three steps: (1) forward linear transformation, (2) identification of the components related to signal and noise subspaces, (3) inverse transformation during which the components that belong to the noise subspace are disregarded, i.e. dimension reduction in the component space. The separation matrix is found based on problem-s…
Characterization of greedy bases in Banach spaces
2017
Abstract We shall present a new characterization of greedy bases and 1-greedy bases in terms of certain functionals defined using distances to one dimensional subspaces generated by the basis. We also introduce a new property that unifies the notions of unconditionality and democracy and allows us to recover a better dependence on the constants.
A dynamical systems study of the inhomogeneous Lambda-CDM model
2010
We consider spherically symmetric inhomogeneous dust models with a positive cosmological constant, $\Lambda$, given by the Lemaitre-Tolman-Bondi metric. These configurations provide a simple but useful generalization of the Lambda-CDM model describing cold dark matter (CDM) and a Lambda term, which seems to fit current cosmological observations. The dynamics of these models can be fully described by scalar evolution equations that can be given in the form of a proper dynamical system associated with a 4-dimensional phase space whose critical points and invariant subspaces are examined and classified. The phase space evolution of various configurations is studied in detail by means of two 2-…
RPA in wavefunction representation
1992
The RPA is formulated in subspaces of coordinate-like and momentum-like I ph operators. This allows to embed a large class of approximative schemes into a generalized RPA treatment. We give a detailed formulation in terms of wavefunctions in coordinate space which is ideally suited to practical programming. In particular, we work out the reduction to spherical tensors in the case of spherical symmetry which is most often the starting point in finite Fermion systems.
Collective subspaces for large amplitude motion and the generator coordinate method
1979
The collection path $|\ensuremath{\varphi}(q)〉$ to be used in a microscopic description of large amplitude collective motion is determined by means of the generator coordinate method. By varying the total energy with respect to $|\ensuremath{\varphi}(q)〉$ and performing an adiabatic expansion a hierarchy of equations is obtained which determines uniquely a hierarchy of collective paths with increasing complexity. To zeroth order the $|\ensuremath{\varphi}(q)〉$ are Slater determinants, to first order they include 2p-2h correlations. In both cases simple noninterative prescriptions for an explicit construction of the path are derived. For a correlated path their solutions agree at the Hartree…
Interaction-free evolution in the presence of time-dependent Hamiltonians
2015
The generalization of the concept of interaction-free evolutions (IFE) [A. Napoli, {\it et al.}, Phys. Rev. A {\bf 89}, 062104 (2014)] to the case of time-dependent Hamiltonians is discussed. It turns out that the time-dependent case allows for much more rich structures of interaction-free states and interaction-free subspaces. The general condition for the occurrence of IFE is found and exploited to analyze specific situations. Several examples are presented, each one associated to a class of Hamiltonians with specific features.