We use Newton divided differences for calculation of Greene sums -- the
rational functions determined by linear extensions of partially ordered sets.
Identities for Greene sums generate relations for Newton divided differences
and Arnold differential forms. Also generalizations of the Newton interpolation
series which are indexed by sequences of partially ordered sets are received.
lunes, 30 de noviembre de 2009
Calculus of linear extensions and Newton interpolation. (arXiv:0911.5620v1 [math.CO])
Coarse space over the ages. (arXiv:0911.5725v1 [math.NA])
The objective of this paper is to explain the principles of the design of a
coarse space in a simplified way and by pictures. The focus is on ideas rather
than on a more historically complete presentation. Also, space limitation does
not allow even to mention many important methods and papers that should be
rightfully included.
On Adaptive-Multilevel BDDC. (arXiv:0911.5730v1 [math.NA])
We combine the advantages of the adaptive and multilevel approaches, proposed
previously by the authors, to propose a new method that preserves both,
parallel scalability with increasing number of subdomains and excellent
convergence properties. Performance of the method is illustrated on a
two-dimensional problem of linear elasticity.
Numerical Study of Liquid Crystal Elastomer Using Mixed Finite Element Method. (arXiv:0911.5415v1 [math.NA])
In this paper, we tried to model the elastic behavior of liquid crystal
elastomer using mixed finite element method. We start from an energy functional
which includes Blandon's stored energy of LCE, penalization of change of
directors, and two Lagrangian terms enforcing incompressibility and the unity
of the directors. The resulting Euler-Lagrange equation is a nonlinear equation
of the displacement ${mathbf u}$, the director ${mathbf n}$, the pressure $p$
and the Lagrange multiplier $lambda$. Inf-sup conditions for the
well-posedness of the linearized system were proposed and some are proved. For
those inf-sup conditions that are not easy to prove, we suggest ways to do the
numerical verification (the inf-sup tests). Finally, some numerical results are
presented.
Quasi-Lp norm orthogonal Galerkin expansions in sums of Jacobi polynomials
Matroid Polytopes and their Volumes
Fast Multiresolution Algorithms and Their Related Variational Problems for Image Denoising
An Iterative Method for Solving Non-Linear Hydromagnetic Equations. (arXiv:0911.5214v1 [math.NA])
We propose an iterative finite element method for solving non-linear
hydromagnetic and steady Euler's equations. Some three-dimensional
computational tests are given to confirm the convergence and the high
efficiency of the method.
Non-convexly constrained linear inverse problems. (arXiv:0911.5098v1 [math.NA])
This paper considers the inversion of ill-posed linear operators. To
regularise the problem the solution is enforced to lie in a non-convex subset.
Theoretical properties for the stable inversion are derived and an iterative
algorithm akin to the projected Landweber algorithm is studied. This work
extends recent progress made on the efficient inversion of finite dimensional
linear systems under a sparsity constraint to the Hilbert space setting and to
more general non-convex constraints.