In the convergence theory of multisplittings for symmetric positive definite (s.p.d.) matrices it is usually assumed that the weighting matrices are scalar matrices, i.e., multiples of the identity. In this paper, this restrictive condition is eliminated. In its place it is assumed that more than one (inner) iteration is performed in each processor (or… (More)
Different types of synchronous and asynchronous two-stage multisplitting algorithms for the solution of linear systems are analyzed. The different algorithms which appeared in the literature are reviewed, and new ones are presented. Convergence properties of these algorithms are studied when the matrix in question is either monotone or an H-matrix. Relaxed… (More)
Block parallel iterative methods for the solution of mildly non-linear systems of equations of the form Ax = Φ(x) are studied. Two-stage methods, where the solution of each block is approximated by an inner iteration , are treated. Both synchronous and asynchronous versions are analyzed, and both pointwise and blockwise convergence theorems provided. The… (More)
The use of block two-stage methods for the iterative solution of consistent singular linear systems is studied. In particular, hypotheses are provided for the convergence of non-stationary methods, i.e., when the number of inner iterations may vary from block to block and from one outer iterations to another.
—Two-stage iterative methods for the solution of linear systems are studied. Convergence of both stationary and nonstationary cases is analyzed when the coefficient matrix is Hermitian positive definite.
Non-stationary multisplitting algorithms for the solution of linear systems are studied. Convergence of these algorithms is analyzed when the coefficient matrix of the linear system is hermitian positive definite. Asyn-chronous versions of these algorithms are considered and their convergence investigated.
Available online xxxx Keywords: GPGPU GPU libraries Multicore architectures Nonlinear conjugate gradient algorithms Parallel preconditioners Bratu problem a b s t r a c t In this work we describe some parallel algorithms for solving nonlinear systems using CUDA (Compute Unified Device Architecture) over a GPU (Graphics Processing Unit). The proposed… (More)
Software reusability has proven to be an effective practice to speed-up the development of complex high-performance scientific and engineering applications. We promote the reuse of high quality software and general purpose libraries through the Advance CompuTational Software (ACTS) Collection. ACTS tools have continued to provide solutions to many of… (More)
Permission to make digital or hard copies of portions of this work for personal or classroom use is granted provided that the copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise requires prior specific permission by the publisher mentioned above.… (More)