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Orthogonal Projection
"... 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 ..."
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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 SobolevKondrashov imbedding theorem (see [PS]). Consider the following mixed problem: Lu = f in Ω, u = u0 on Γ ⊆ ∂Ω, meas(Γ)> 0 (1)
Products Of Orthogonal Projections
, 1997
"... . 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. Introdu ..."
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Cited by 3 (0 self)
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. 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
ORTHOGONAL PROJECTION REGULARIZATION OPERATORS
"... Abstract. Tikhonov regularization often is applied with a finite difference regularization operator that approximates a loworder derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference operators ..."
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Cited by 9 (9 self)
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Abstract. Tikhonov regularization often is applied with a finite difference regularization operator that approximates a loworder derivative. This paper proposes the use of orthogonal projections as regularization operators, e.g., with the same null space as commonly used finite difference
PRODUCTS OF ORTHOGONAL PROJECTIONS TIMUR OIKHBERG
"... 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. ..."
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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.
ON DIAGONALLYRELAXED ORTHOGONAL PROJECTION METHODS
, 2005
"... Abstract. We propose and study a blockiterative projections method for solving linear equations and/or inequalities. The method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonallyrelaxed or ..."
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Cited by 15 (8 self)
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Abstract. We propose and study a blockiterative projections method for solving linear equations and/or inequalities. The method allows diagonal componentwise relaxation in conjunction with orthogonal projections onto the individual hyperplanes of the system, and is thus called diagonallyrelaxed
On the orthogonal projection of a belief function
"... 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 distri ..."
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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
Products of orthogonal projections and polar decompositions
 Linear Algebra Appl
"... 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 MoorePenrose pseudoinverses of elements of X. ..."
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Cited by 6 (1 self)
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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 MoorePenrose pseudoinverses of elements of X.
On The Spectra Of Sums Of Orthogonal Projections With Applications To Parallel Computing
, 1991
"... 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 the c ..."
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Cited by 33 (3 self)
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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
GENERALIZED ORTHOGONAL PROJECTIONS AND SHORTED OPERATORS
"... Dedicated to the memory of our friend Chicho Guadalupe Abstract. Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and 〈 , 〉A: H×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉, ξ, η ∈ H. Given T ∈ L(H), T is Aselfadjoint if AT ..."
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selfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of Aselfadjoint projections onto S,
Results 1  10
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2,548