The completion of matrices with missing values under the rank constraint is a non-convex optimization problem. A popular convex relaxation is based on minimization of the nuclear norm (sum of singular values) of the matrix. For this relaxation, an important question is whether the two optimization problems lead to the same solution. This question was addressed in the literature mostly in the ca...

In this paper we present the results obtained in solving consistent sparse systems of n nonlinear equations F(x) = 0; by a Quasi-Newton method combined with a p block iterative row-projection linear solver of Cimmino-type, 1 p n: Under weak regularity conditions for F; it is proved that this Inexact Quasi-Newton method has a local, linear convergence in the energy norm induced by the preconditi...

Let X be an operator space, let φ be a product on X , and let (X, φ) denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping φ for the algebra (X, φ) to have a completely isometric representation as an algebra of operators on some Hilbert space. In particular, we give an elegant geometrical characterization of such products by using the Haagerup ...

We analyze the approximation order associated with a directed set of spaces, {Sh}h>0, each of which spanned by the hZZ-translates of one compactly supported function φh : IR s → C. Under a regularity condition on the sequence {φh}h, we show that the optimal approximation order (in the ∞-norm) is always realized by quasi-interpolants, hence in a linear way. These quasi-interpolants provide the b...

In this paper, Newton-multigrid scheme on adaptive finite element discretisation is employed for solving elliptic quasi-variational inequalities with nonlinear source terms. We use Newton’s method as the outer iteration standard linearization, and using multigrid inner solution of Jacobian system at each step. The uniform convergence methods shown in sense that have a contraction number respect...

We consider a minimal residual discretization of simultaneous space-time variational formulation parabolic evolution equations. Under the usual ‘LBB’ stability condition on pairs trial- and test spaces we show quasi-optimality numerical approximations without assuming symmetry spatial part differential operator. stronger LBB error estimates in an energy-norm that are independent this

In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective funct...

In this paper, we investigate the approximation of a diffusion model problem with contrasted diffusivity for various nonconforming methods. The essential difficulty is that Sobolev smoothness index exact solution may be just barely larger than 1. lack handled by giving weak meaning to normal derivative at mesh faces. We derive robust and quasi-optimal error estimates. Quasi-optimality means bou...