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A simple regularization method for the ill-posed evolution equation

Nguyen Huy Tuan, Dang Duc Trong (2011)

Czechoslovak Mathematical Journal

The nonhomogeneous backward Cauchy problem u t + A u ( t ) = f ( t ) , u ( T ) = ϕ , where A is a positive self-adjoint unbounded operator which has continuous spectrum and f is a given function being given is regularized by the well-posed problem. New error estimates of the regularized solution are obtained. This work extends earlier results by N. Boussetila and by M. Denche and S. Djezzar.

A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation

O. Awono, J. Tagoudjeu (2010)

Mathematical Modelling of Natural Phenomena

We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...

A spectral mapping theorem for Banach modules

H. Seferoğlu (2003)

Studia Mathematica

Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then σ ( T μ ) = μ ̂ ( s p ( X ) ) ¯ for each measure μ in reg(M(G)), where T μ denotes the operator in B(X) defined by T μ x = μ x , σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal I X = f L ¹ ( G ) | T f = 0 , μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all...

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