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On mesh independence and Newton-type methods

Owe Axelsson (1993)

Applications of Mathematics

Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters H and h for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...

On Minimizing ||S−(AX−XB)||Pp

Mecheri, Salah (2000)

Serdica Mathematical Journal

In this paper, we minimize the map Fp (X)= ||S−(AX−XB)||Pp , where the pair (A, B) has the property (F P )Cp , S ∈ Cp , X varies such that AX − XB ∈ Cp and Cp denotes the von Neumann-Schatten class.

On monotone minimal cuscos

Karel Pastor, Dušan Bednařík (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On monotone-like mappings in Orlicz-Sobolev spaces

Vesa Mustonen, Matti Tienari (1999)

Mathematica Bohemica

We study the mappings of monotone type in Orlicz-Sobolev spaces. We introduce a new class ( S m ) as a generalization of ( S + ) and extend the definition of quasimonotone map. We also prove existence results for equations involving monotone-like mappings.

On monotonic solutions of an integral equation of Abel type

Mohamed Abdalla Darwish (2008)

Mathematica Bohemica

We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C [ 0 , 1 ] . The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

On monotonic solutions of some integral equations

J. Caballero, Donal O'Regan, K. B. Sadarangani (2005)

Archivum Mathematicum

The aim of this paper is to obtain monotonic solutions of an integral equation of Urysohn-Stieltjes type in C [ 0 , 1 ] . Existence will be established with the aid of the measure of noncompactness.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Umarov, Sabir, Gorenflo, Rudolf (2005)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.* Supported by German Academic Exchange Service (DAAD).

On multilinear generalizations of the concept of nuclear operators

Dahmane Achour, Ahlem Alouani (2010)

Colloquium Mathematicae

This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear mapping...

On multilinear mappings of nuclear type.

Mário C. Matos (1993)

Revista Matemática de la Universidad Complutense de Madrid

The space of multilinear mappings of nuclear type (s;r1,...,rn) between Banach spaces is considered, some of its properties are described (including the relationship with tensor products) and its topological dual is characterized as a Banach space of absolutely summing mappings.

On multilinear singular integrals of Calderón-Zygmund type.

Loukas Grafakos, Rodolfo H. Torres (2002)

Publicacions Matemàtiques

A variety of results regarding multilinear singular Calderón-Zygmund integral operators is systematically presented. Several tools and techniques for the study of such operators are discussed. These include new multilinear endpoint weak type estimates, multilinear interpolation, appropriate discrete decompositions, a multilinear version of Schur's test, and a multilinear version of the T1 Theorem suitable for the study of multilinear pseudodifferential and translation invariant operators. A maximal...

Currently displaying 481 – 500 of 1573