Parallel Complexity Of Linear System Solution
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| Author | : Bruno Codenotti |
| Publisher | : World Scientific |
| Total Pages | : 232 |
| Release | : 1991-04-30 |
| Genre | : Computers |
| ISBN | : 9814506478 |
This book presents the most important parallel algorithms for the solution of linear systems. Despite the evolution and significance of the field of parallel solution of linear systems, no book is completely dedicated to the subject. People interested in the themes covered by this book belong to two different groups: numerical linear algebra and theoretical computer science, and this is the first effort to produce a useful tool for both. The book is organized as follows: after introducing the general features of parallel algorithms and the most important models of parallel computation, the authors analyze the complexity of solving linear systems in the circuit, PRAM, distributed, and VLSI models. The approach covers both the general case (i.e. dense linear systems without structure) and many important special cases (i.e. banded, sparse, Toeplitz, circulant linear systems).
| Author | : Bruno Codenotti |
| Publisher | : World Scientific |
| Total Pages | : 234 |
| Release | : 1991 |
| Genre | : Computers |
| ISBN | : 9789810205034 |
This book presents the most important parallel algorithms for the solution of linear systems. Despite the evolution and significance of the field of parallel solution of linear systems, no book is completely dedicated to the subject. People interested in the themes covered by this book belong to two different groups: numerical linear algebra and theoretical computer science, and this is the first effort to produce a useful tool for both. The book is organized as follows: after introducing the general features of parallel algorithms and the most important models of parallel computation, the authors analyze the complexity of solving linear systems in the circuit, PRAM, distributed, and VLSI models. The approach covers both the general case (i.e. dense linear systems without structure) and many important special cases (i.e. banded, sparse, Toeplitz, circulant linear systems).
| Author | : James M. Ortega |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 309 |
| Release | : 2013-06-29 |
| Genre | : Computers |
| ISBN | : 1489921125 |
Although the origins of parallel computing go back to the last century, it was only in the 1970s that parallel and vector computers became available to the scientific community. The first of these machines-the 64 processor llliac IV and the vector computers built by Texas Instruments, Control Data Corporation, and then CRA Y Research Corporation-had a somewhat limited impact. They were few in number and available mostly to workers in a few government laboratories. By now, however, the trickle has become a flood. There are over 200 large-scale vector computers now installed, not only in government laboratories but also in universities and in an increasing diversity of industries. Moreover, the National Science Foundation's Super computing Centers have made large vector computers widely available to the academic community. In addition, smaller, very cost-effective vector computers are being manufactured by a number of companies. Parallelism in computers has also progressed rapidly. The largest super computers now consist of several vector processors working in parallel. Although the number of processors in such machines is still relatively small (up to 8), it is expected that an increasing number of processors will be added in the near future (to a total of 16 or 32). Moreover, there are a myriad of research projects to build machines with hundreds, thousands, or even more processors. Indeed, several companies are now selling parallel machines, some with as many as hundreds, or even tens of thousands, of processors.
| Author | : Yousef Saad |
| Publisher | : SIAM |
| Total Pages | : 546 |
| Release | : 2003-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780898718003 |
Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of the new generation of linear and nonlinear systems arising in typical applications has grown. Solving the three-dimensional models of these problems using direct solvers is no longer effective. At the same time, parallel computing has penetrated these application areas as it became less expensive and standardized. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. Iterative Methods for Sparse Linear Systems, Second Edition gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.
| Author | : D. A. Reed |
| Publisher | : |
| Total Pages | : 52 |
| Release | : 1984 |
| Genre | : Iterative methods (Mathematics) |
| ISBN | : |
"The suitability of different parallel architectures for solving randomly sparse linear systems is discussed. Based on the complexity of task scheduling, one parallel architecture, based on a broadcast bus, is presented and analyzed" -- abstract.
| Author | : Robert Bernard Armistead |
| Publisher | : |
| Total Pages | : 96 |
| Release | : 2010 |
| Genre | : |
| ISBN | : |
Solving sparse systems of linear equations permeates power system analysis. Newton-Raphson, decoupled, and fast decoupled algorithms all require the repeated solving of sparse systems of linear equations in order to capture the steady state operational conditions of the power system under test. Solving these systems of equations is usually done using LU Factorization which has an order of complexity O(n3) where n represents the number of equations in the system. The Chio's condensation algorithm is an alternative approach, which in general has a complexity of O(n4). However, it has a straightforward formulation that can be easily implemented in a parallel computing architecture. Previous research has not investigated the application of the Chio's algorithm under sparse matrix, which is typical for power system analysis. This thesis presents a MPI-based parallel solution of sparse linear systems using Chio's condensation algorithm and realistic test data from power flow analysis. Different sparse matrix techniques are discussed, and a reordering scheme is applied to further improve the efficiency for solving the sparse linear system.
| Author | : Howard Fu-Hwa Ko |
| Publisher | : |
| Total Pages | : 462 |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : Gerard Meurant |
| Publisher | : Elsevier |
| Total Pages | : 777 |
| Release | : 1999-06-16 |
| Genre | : Mathematics |
| ISBN | : 0080529518 |
This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
| Author | : Garry Rodrigue |
| Publisher | : Elsevier |
| Total Pages | : 416 |
| Release | : 2014-05-10 |
| Genre | : Reference |
| ISBN | : 1483276643 |
Parallel Computations focuses on parallel computation, with emphasis on algorithms used in a variety of numerical and physical applications and for many different types of parallel computers. Topics covered range from vectorization of fast Fourier transforms (FFTs) and of the incomplete Cholesky conjugate gradient (ICCG) algorithm on the Cray-1 to calculation of table lookups and piecewise functions. Single tridiagonal linear systems and vectorized computation of reactive flow are also discussed. Comprised of 13 chapters, this volume begins by classifying parallel computers and describing techniques for performing matrix operations on them. The reader is then introduced to FFTs and the tridiagonal linear system as well as the ICCG method. Different versions of the conjugate gradient method for solving the time-dependent diffusion equation are considered. Subsequent chapters deal with two- and three-dimensional fluid flow calculations, paying particular attention to the principal issues in designing efficient numerical methods for hydrodynamic calculations; the decisions that a numerical modeler must make to optimize chemically reactive flow simulations; and how to handle disk-to-core data transfer and storage allocation for the solution of the implicit equations for three-dimensional flows. The book also describes the time-split finite difference scheme for solving the two-dimensional Navier-Stokes equation for flows through slotted nozzles. Finally, the large-scale stimulation of plasmas, as carried out on a small computer with an array processor, is discussed. This monograph should be of interest to specialists in computer science.
| Author | : Avi Lin |
| Publisher | : |
| Total Pages | : 24 |
| Release | : 1990 |
| Genre | : Linear systems |
| ISBN | : |
