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J. Inverse Ill-Posed Probl. 21 (2013), 781–797 DOI 10.1515/ jip-2012-0004 © de Gruyter 2013 On accuracy of solving Symm’s equation by a fully discrete projection method Sergey G. Solodky and Evgeniya V. Semenova Abstract. A problem of an approximate solving of Symm’s integral equation for an in- finitely smooth closed boundary is considered. For a fully discrete projection method, error estimates are found in the metric of Sobolev spaces. A discretization parameter is chosen by balancing principle. Keywords. Symm’s integral equation, fully discrete projection

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, Vol.7(2007), No.3, pp.255–263 c© 2007 Institute of Mathematics of the National Academy of Sciences of Belarus ERROR BOUNDS OF A FULLY DISCRETE PROJECTION METHOD FOR SYMM’S INTEGRAL EQUATION S.G. SOLODKY1 AND E. V. LEBEDEVA2 Abstract — The approximation properties of a fully discrete projection method for Symm’s integral equation with a infinite smooth boundary have been investigated. For the method, error bounds have been found in the metric of Sobolev’s spaces. The method turns out to be more accurate compared to the

Studies in Nonlinear Dynamics & Econometrics Volume 9, Issue 2 2005 Article 3 Solving Ramsey Problems with Nonlinear Projection Methods Michael T. Gapen∗ Thomas F. Cosimano† ∗International Monetary Fund, mgapen@imf.org †University of Notre Dame, tcosiman@nd.edu All rights reserved. No part of this publica- tion may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permis- sion of the publisher, bepress, which has been given certain

In this paper, we consider some issues related to application of a projection method to calculation of the numerical solution to the nonlinear kinetic Boltzmann equation using the Monte Carlo method [ 4 ]. The justification of this approach is based on the Chentsov theorem [ 2 ] which states that the norm of the square of the projection error in L 2 is equal to the sum of the square of the norm of systematic error and the square of the norm of random error. Previously, in [ 10 ], a projection method was applied to the numerical solution of the problem of

J. Inverse Ill-Posed Probl. 2016; 24 (3):323–332 Research Article Mikhali Y. Kokurin* Stable gradient projection method for nonlinear conditionally well-posed inverse problems Abstract: We study the standard gradient projection method in a Hilbert space, as applied to minimization of the residual functional for nonlinear operator equations with dierentiable operators. The functional is minimized over a closed, convex and bounded set, which contains a solution to the equation. It is assumed that the inverse problemassociatedwith the operator equation is

Abstract

We present an adaptation of the (by now classical) parallel projection method for finding a point in the nonempty intersection of a finite number of closed convex sets in a Hilbert space. The adaptation consists of controlling at each iteration step whether or not some condition is fulfilled; if not, the adapted next iteration point is determined such that its position with respect to the intersection is better than the usual next iteration point. This may improve the speed of convergence.

Abstract

In this paper, we firstly introduce a viscosity projection method for the class T mappings

xn+1=αnPH(xn, Snxn) f(xn) + (1-αn)Snxn,

where Sn = (1 - w)I + wTn, w ∈ (0; 1); Tn ∈ T and prove strong convergence theorems of the proposed method. It is verified that the viscosity projection method converges locally faster than the viscosity method. Furthermore, we present a viscosity projection method for a quasi-nonexpansive and nonexpansive mappings in Hilbert spaces. A numerical test provided in the paper shows that the viscosity projection method converges faster than the viscosity method.

Chapter 5. Projection method 5.1. I N T R O D U C T I O N In this chapter we study the problem of reconstructing the two-dimensional parameter in the oscillation and acoustic equation. In both cases, the in- verse problem is considered in the form of a nonlinear system of Volterra integral equations. We establish the convergence of the projection method and estimate the rate of convergence. The idea of the projection method of solving multidimensional inverse problem (Kabanikhin, 1988b) is as follows: two variables, the time variable t and the output

Monte Carlo Methods Appl. 16 (2010), 343–359 DOI 10.1515/MCMA.2010.020 © de Gruyter 2010 Stochastic iterative projection methods for large linear systems Karl Sabelfeld and Nadja Loshchina Abstract. We suggest a randomized version of the projection methods belonging to the class of a “row-action” methods which work well both for systems with quadratic nonsin- gular matrices and for overdetermined systems. These methods belong to a type known as Projection on Convex Sets methods. Here we present a method beyond the conventional Markov chain based Neumann

Aloisia Moser Hegel’s Speculative Method and Wittgenstein’s Projection Method Abstract Against the widely held but contradictory ideas that (a) there is no method in Wittgenstein and that (b) the picture theory is at the heart of the Trac- tatus, I argue that the center of the Tractatus is Wittgenstein’s projection method, a method which shows us how propositions can have sense when they are used or, to put it another way are projected onto reality. I argue that we do not find in the Tractatus a static picture theory, as the common reading of the Tractatus has us