Andreas Frommer

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Asynchronous iterations arise naturally on parallel computers if one wants to minimize idle times. This paper reviews certain models of asynchronous iterations, using a common theoretical framework. The corresponding convergence theory and various domains of applications are presented. These include nonsingular linear systems, nonlinear systems, and initial(More)
We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the di€usion type. Within this framework we develop a new Optimal Polynomial Scheme (OPS) which we show to terminate within a ®nite number m of steps, where m only depends on the graph and not on the initial load distribution. We show that all(More)
Weighted max-norm bounds are obtained for Algebraic Additive Schwarz Iterations with overlapping blocks for the solution of Ax = b, when the coefficient matrix A is an M -matrix. The case of inexact local solvers is also covered. These bounds are analogous to those that exist using A-norms when the matrix A is symmetric positive definite. A new theorem(More)
Tikhonov–Phillips regularization is one of the best-known regularization methods for inverse problems. A posteriori criteria for determining the regularization parameter α require solving (∗) (AA+ αI)x = Ay for different values of α. We investigate two methods for accelerating the standard cg-algorithm for solving the family of systems (∗). The first one(More)
1 Department ofMathematics andComputerScience,EmoryUniversity,Atlanta,GA30322, USA; e-mail: benzi@mathcs.emory.edu 2 Fachbereich Mathematik, Universität Wuppertal, 42097 Wuppertal, Germany; e-mail: frommer@math.uni-wuppertal.de 3 Fakultät für Mathematik, Universität Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany; e-mail:(More)
Convergence results for the restrictive additive Schwarz (RAS) method of Cai and Sarkis [SIAM J. Sci. Comput., 21 (1999), pp. 792–797] for the solution of linear systems of the form Ax = b are provided using an algebraic view of additive Schwarz methods and the theory of multisplittings. The linear systems studied are usually discretizations of partial(More)
We consider a seed system Ax = b together with a shifted linear system of the form We develop modifications of the BiCGStab(ℓ) method which allow to solve the seed and the shifted system at the expense of just the matrix-vector multiplications needed to solve Ax = b via BiCGStab(ℓ). On the shifted system, these modifications do not perform the corresponding(More)
We discuss iterative nearest neighbor load balancing schemes on processor networks which are represented by a cartesian product of graphs like e.g. tori or hypercubes. By the use of the Alternating-Direction Loadbalancing scheme, the number of load balance iterations decreases by a factor of 2 for this type of graphs. The resulting ow is analyzed(More)