Our aim is to present a numerical method for solving elliptical problems by theoretical discretization. In order to do it, a complete system of eigenfunctions of the Laplacean and the compact imbedding of H 1 (Ω) in L 2 (Ω) are used in the paper. Let Ω be a bounded domain in R M, with a quite smooth boundary such that we can apply the Green’s formula and the Sobolev-Kondrashov imbedding theorem (see [PS]). Consider the following mixed problem: Lu = f in Ω, u = u0 on Γ ⊆ ∂Ω, meas(Γ)> 0 (1)

. We give a characterization of operators on a separable Hilbert space of norm less than one that can be represented as products of orthogonal projections and give an estimate on the number of factors. We also describe the norm closure of the set of all products of orthogonal projections. 1

Abstract. Tikhonov regularization often is applied with a finite difference regularization operator that approximates a low-order derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference

Abstract. We give a characterization of operators on a separable Hilbert space of norm less than one that can be represented as products of orthogonal projections and give an estimate on the number of factors. We also describe the norm closure of the set of all products of orthogonal projections. 1.

Abstract. We propose and study a block-iterative projections method for solving linear equations and/or inequalities. The method allows diagonal component-wise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonallyrelaxed

Abstract. In this paper we study a new probability associated with any given belief function b, i.e. the orthogonal projection π[b] of b onto the probability simplex P. We provide an interpretation of π[b] in terms of a redistribution process in which the mass of each focal element is equally

Abstract We characterize the sets X of all products P Q, and Y of all products P QP , where P, Q run over all orthogonal projections and we solve the problems arg min{ P − Q : (P, Q) ∈ Z}, for Z = X or Y. We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of X.

Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while

-selfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S,

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