Distributed Sparse Gaussian Elimination and Orthogonal Factorization


Book Description

Abstract: "We consider the solution of a linear system Ax = b on a distributed memory machine when the matrix A has full rank and is large, sparse and nonsymmetric. We use our Cartesian Nested Dissection algorithm to compute a fill-reducing column ordering of the matrix. We develop algorithms that use the associated separator tree to estimate the structure of the factor and to distribute and perform numeric computations. When the matrix is nonsymmetric but square, the numeric computations involve Gaussian elimination with row pivoting; when the matrixis overdetermined, row-oriented Householder transforms are applied to compute the triangular factor of an orthogonal factorization. We compare the fill incurred by our approach to that incurred by well known sequential methods and report on the performance of our implementation on the Intel iPSC/860."




Matrix Computations


Book Description

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.




Parallel Computing in Optimization


Book Description

During the last three decades, breakthroughs in computer technology have made a tremendous impact on optimization. In particular, parallel computing has made it possible to solve larger and computationally more difficult prob lems. This volume contains mainly lecture notes from a Nordic Summer School held at the Linkoping Institute of Technology, Sweden in August 1995. In order to make the book more complete, a few authors were invited to contribute chapters that were not part of the course on this first occasion. The purpose of this Nordic course in advanced studies was three-fold. One goal was to introduce the students to the new achievements in a new and very active field, bring them close to world leading researchers, and strengthen their competence in an area with internationally explosive rate of growth. A second goal was to strengthen the bonds between students from different Nordic countries, and to encourage collaboration and joint research ventures over the borders. In this respect, the course built further on the achievements of the "Nordic Network in Mathematical Programming" , which has been running during the last three years with the support ofthe Nordic Council for Advanced Studies (NorFA). The final goal was to produce literature on the particular subject, which would be available to both the participating students and to the students of the "next generation" .




Parallel Numerical Algorithms


Book Description

In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.




LAPACK Users' Guide


Book Description

LAPACK is a library of numerical linear algebra subroutines designed for high performance on workstations, vector computers, and shared memory multiprocessors. Release 3.0 of LAPACK introduces new routines and extends the functionality of existing routines.




Proceedings


Book Description










Introduction to Parallel Computing


Book Description

Mathematics of Computing -- Parallelism.




CONPAR 90 - VAPP IV


Book Description

Parallel architectures are no longer pure research vehicles, as they were some years ago. There are now many commercial systems competing for market segments in scientific computing. The 1990s are likely to become the decade of parallel processing. CONPAR 90 - VAPP IV is the joint successor meeting of two highly successful international conference series in the field of vector and parallel processing. This volume contains the 79 papers presented at the conference. The various topics of the papers include hardware, software and application issues. Some of the session titles best reflect the contents: new models of computation, logic programming, large-grain data flow, interconnection networks, communication issues, reconfigurable and scalable systems, novel architectures and languages, high performance systems and accelerators, performance prediction / analysis / measurement, performance monitoring and debugging, compile-time analysis and restructurers, load balancing, process partitioning and concurrency control, visualization and runtime analysis, parallel linear algebra, architectures for image processing, efficient use of vector computers, transputer tools and applications, array processors, algorithmic studies for hypercube-type systems, systolic arrays and algorithms. The volume gives a comprehensive view of the state of the art in a field of current interest.