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We design a general mathematical framework to analyze the properties of nearest neighbor balancing algorithms of the diiusion 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)

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)

We present methods to compute verified square roots of a square matrix A. Given an approximation X to the square root, obtained by a classical floating point algorithm, we use interval arithmetic to find an interval matrix which is guaranteed to contain the error of X. Our approach is based on the Krawczyk method which we modify in two different ways in… (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)

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 (*) (A * A + αI)x = A * y δ for different values of α. We investigate two methods for accelerating the standard cg-algorithm for solving the family of systems (*). The… (More)

The convergence of multiplicative Schwarz-type methods for solving linear systems when the coefficient matrix is either a nonsingular M-matrix or a symmetric positive definite matrix is studied using classical and new results from the theory of splittings. The effect on convergence of algorithmic parameters such as the number of subdomains, the amount of… (More)