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Abstract.This paper presents a self-stabilizing algorithm that finds the bridge-connected components of a connected undirected graph on an asynchronous distributed or network model of computation. An edge of a graph is a bridge if its removal disconnects the graph. The bridge-connected components problem consists of finding the maximal connected subgraphs (components) of the given graph such that...
Abstract.Discrete-time relaxation methods based on direct quadrature methods for the numerical solution of second kind Volterra systems are proposed. The convergence of the discrete-time iterations is analyzed.
Abstract.We consider a non-overlapping domain decomposition method for diffusion-reaction problems which is known to converge strongly from previous work. We derive an a posteriori estimate which bounds the errors on the subdomains by the difference of traces of the subdomain solutions. If the domain decomposition method is discretized by finite elements we can adapt the techniques of the usual a...
In this paper we present iteration methods of Halleys type for the simultaneous inclusion of all zeros of a polynomial. Using the concept of the R-order of convergence of mutually dependent sequences, we present the convergence analysis for the total-step and the single-step methods with Newtons corrections. The suggested algorithms possess a great computational efficiency since the increase of the...
Abstract.In this paper we prove relations between the eigenvalues of matrices that occur during the solution of linear programming problems with interior-point methods. We will present preconditioners for these matrices that preserve the relations and discuss the practical implications of our results when iterative linear solvers are used.
Abstract. Second order ordinary differential equations of the form with and A, B, C and D functions of x and y are of special interest because they may allow the largest possible group of point symmetries if its coefficients satisfy certain constraints. For large classes of these equations a solution algorithm is described that determines its general solution in...
Abstract.We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degree in dimension d, we need about function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyaks technique. We also compare different methods to obtain formulas with high trigonometric...
Abstract.A class of matrices ( -matrices) is introduced which have the following properties. (i) They are sparse in the sense that only few data are needed for their representation. (ii) The matrix-vector multiplication is of almost linear complexity. (iii) In general, sums and products of these matrices are no longer in the same set, but their truncations to the -matrix format are again...
Abstract.Iterative methods with variable preconditioners of additive type are proposed. The scaling factors of each summand in the additive preconditioners are optimized within each iteration step. It is proved that the presented methods converge at least as fast as the Richardsons iterative method with the corresponding additive preconditioner with optimal scaling factors. In the presented numerical...
Abstract.In this paper we consider a special nonlinear total least squares problem, where the model function is of the form . Using the fact that after an appropriate substitution, the model function becomes linear in parameters, and that the symmetry preserves the distances, this nonlinear total least squares problem can be greatly simplified. In this paper we give the existence...
Abstract.We propose a modification of Newtons method for computing multiple roots of systems of analytic equations. Under mild assumptions the iteration converges quadratically. It involves certain constants whose product is a lower bound for the multiplicity of the root. As these constants are usually not known in advance, we devise an iteration in which not only an approximation for the root is...
Abstract.The coupling of nonconforming finite element and boundary element methods was established in Part I of this paper, where quasi-optimal a priori error estimates are provided. In the second part, we establish sharp a posteriori error estimates and so justify adaptive mesh-refining algorithms for the efficient numerical treatment of transmission problems with the Laplacian in unbounded domains.
Abstract.We propose a fast iterative method to optimize coarse basis functions in algebraic multigrid by minimizing the sum of their energies, subject to the condition that linear combinations of the basis functions equal to given zero energy modes, and subject to restrictions on the supports of the coarse basis functions. For a particular selection of the supports, the first iteration gives exactly...
Abstract.Nonconforming finite element methods are sometimes considered as a variational crime and so we may regard its coupling with boundary element methods. In this paper, the symmetric coupling of nonconforming finite elements and boundary elements is established and a priori error estimates are shown. The coupling involves a further continuous layer on the interface in order to separate the nonconformity...
Abstract.This paper investigates two different semi on-line scheduling problems on a two-machine system. In the first case, we assume that all jobs have their processing times in between p and rp . In the second case, we assume that the largest processing time is known in advance. We show that one has a best possible algorithm with worst case ratio 4/3 while LS is still the best possible...
Abstract.Given an sparse symmetric matrix, we consider the problem of finding the permutation of rows and columns which minimizes the bandwidth. This problem is known to be NP-complete therefore no algorithm polynomial in m is likely to exist. We present two algorithms which exhaustively enumerate all permutations trying to discard as early as possible those which cannot lead to an optimal...
. Image processing of synthetic aperture radar (SAR) images is challenging due to distributed storage of input data sets and since appropriate algorithms are complex and time-consuming. Computers able to process these data in acceptable time usually are not at user's site. Our Concurrent and Distributed Image Processing (CDIP) system overcomes these problems and provides a platform-independent, transparent...
Abstract.Image processing of synthetic aperture radar (SAR) images is challenging due to distributed storage of input data sets and since appropriate algorithms are complex and time-consuming. Computers able to process these data in acceptable time usually are not at users site. Our Concurrent and Distributed Image Processing (CDIP) system overcomes these problems and provides a platform-independent,...
. In line image understanding a minimal line property preserving (MLPP) graph of the image compliments the structural information in geometric graph representations like the run graph. With such a graph and its dual it is possible to efficiently detect topological features like loops and holes and to make use of relations like containment. We present a new rule based method on dual graph contraction...
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