Parallel algorithms for dense linear algebra computations k. Parallel eigenvalue and singular value computations. Written by an authority in the field, this book provides an introduction to the design and analysis of parallel algorithms. A task is a program, its local memory, and a collection of io ports. Parallel optimization algorithms for a problem with very. Computational resolution enhancement superresolution is generally regarded as a memory intensive process due to the large matrixvector calculations involved. Gallivan, 9780898712605, available at book depository with free delivery worldwide. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including 1 direct solution of dense, structured, or sparse linear systems. Parallel prefix computations parallel matrixvector product parallel matrix multiplication pointer jumping summary. The purpose of the workshop is to discuss recent developments in various aspects of parallel matrix algorithms and to bring together mathematicians, computational scientists and engineers. Parallel algorithms have been developed since the 1960s, although no parallel architectures had been constructed at that time see, for example 1, 4, 6. Modeling parallel computations is more complicated than modeling sequential computations because in practice parallel computers tend to vary more in organization than do sequential computers. Parallel algorithms for matrix computations society for.
Data parallel algorithms parallel computers with tens of thousands of processors are typically programmed in a data parallel style, as opposed to the control parallel style used in multiprocessing. This book presents 23 selfcontained chapters, including surveys, written by distinguished researchers in the field of parallel computing. Models, complexity measures, and some simple algorithms models complexity measures examples. The emphasis is on the application of the pram parallel random access machine model of parallel computation, with all its variants, to algorithm analysis.
A simple parallel dense matrixmatrix multiplication. Similarly, many computer science researchers have used a socalled parallel randomaccess. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Algorithms for matrix multiplication, parallel processing, 1993. Parallel cholesky factorization of a block tridiagonal matrix. Often the parallel algorithms are not just a straightforward modi. It has been a tradition of computer science to describe serial algorithms in abstract machine models, often the one known as randomaccess machine. Parallel algorithms for dense linear algebra computations author. For each algorithm we give a brief description along with its complexity in terms of asymptotic work and parallel depth. A library of parallel algorithms this is the toplevel page for accessing code for a collection of parallel algorithms. Part i deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Due to their regular structure, parallel computations involving matrices and vectors readily lend themselves to datadecomposition. Contents preface xiii list of acronyms xix 1 introduction 1 1.
Parallel algorithms for matrix computations guide books. It also deals with the development of parallel algorithms for special linear systems such as banded,vandermonde,toeplitz,and block toeplitz systems. Parallel algorithms for certain matrix computations sciencedirect. It would appear that the parallel time can be made arbitrarily small by making the decomposition finer in granularity. In section 6 we describe some good parallel algorithms for these problems. Dense matrix multiplication cse633 parallel algorithms.
Part ii is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singularvalue decomposition. Parallel scientific computing and optimization springerlink. This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations. Parallel algorithms for banded linear systems siam.
We first consider a onedimensional, columnwise decomposition in which each task encapsulates corresponding columns from a, b, and c. This shows formally that a matrix multiplication algorithm which works for matrices. Analysis of a class of parallel matrix multiplication. While executing the parallel algorithm of matrixvector multiplication, it is.
Parallel optimization algorithms for a problem with very expensive objective function. Course notes parallel algorithms wism 459, 20192020. Describes a selection of important parallel algorithms for matrix computations. In computer science, a parallel algorithm, as opposed to a traditional serial algorithm, is an algorithm which can do multiple operations in a given time. Heath and edgar solomonik parallel numerical algorithms 1 77. Introduction there is a wide body of literature on both theoretical and practical aspects of clas sical matrix computations. One parallel algorithm makes each task responsible for all computation associated with its. The previous section laid the foundation for the analysis of a class of parallel matrixmatrix multiplication algorithms.
Parallel matrix multiplication ut cs the university of. Parallel algorithms are highly useful in processing huge volumes of data in quick time. The algorithms are implemented in the parallel programming language nesl and developed by the scandal project. Parallel algorithms algorithms and data structures. Parallel algorithms lecture 4 matrix operation september 20, 1999. Because the term dataflow is used variously in the literature it is important that we specify at the outset what we mean by it. A parallel algorithm can be executed simultaneously on many different processing devices and then combined together to get the correct result. Students will learn how to design a parallel algorithm for a problem from the area of scientific computing and how to write a parallel program that solves the problem. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including 1 direct solution of dense, structured, or sparse linear systems, 2 dense or structured least squares computations, 3 dense or structured eigenvaluen and singular value computations, and 4 rapid elliptic solvers. Walker2 mathematical sciences section oak ridge national laboratory. Parallel algorithms for certain matrix computations i. Parallel algorithms and data structures cs 448, stanford. Summa algorithm works in on 2 in the parallel environment.
We show that different blockings of the operands lead to different algorithms, each of which can be built from a simple parallel matrixmatrix multiplication kernel. As parallelprocessing computers have proliferated, interest has increased in parallel algorithms. And matrix multiplication that can be done on simd processors in onlogn times. This paper exposes a system atic path that leads from parallel algorithms for matrixvector multiplication. We do not concern ourselves here with the process by which these algorithms are derived or with their efficiency. Keywordsmatrix computations, parallel algorithms, computational. Let us consider two parallel matrix multiplication algorithms. Matrixmatrix product parallel numerical algorithms chapter 3 dense linear systems section 3. Parallel gpu algorithms for asynchronous cellular automata. As a consequence, a large portion of the research on parallel algorithms has gone into the. Publication date 1990 topics matrices data processing, algorithms, parallel processing electronic computers publisher philadelphia. The success of data parallel algorithmseven on problems that at.
This book covers parallel algorithms for a wide range of matrix computation problems, ranging from solving systems of linear equations to computing pseudospectra of matrices. Introduction there is a wide body of literature concerning parallel algorithms, also in the area of numerical linear algebra. Suitable parallel algorithms and systems software are needed to realise the capabilities of parallel computers. I theoretical computer science 180 3997 287308 l there exist olog2 n n order of the input matrix time algorithms for the parallel random access machine pram model. Parallel matrix transpose algorithms on distributed memory concurrent computers jaeyoung choi, jack j. Run sequential algorithm on a single processor core. Parallel methods for solving large sparse or dense linear systems of equations. Parallel algorithms for certain matrix computations. For example, in the case of multiplying a dense matrix with a vector, there can be no more than n2. In the latter case, the algorithms rely on basic matrix computations that can be performed efficiently also on realistic machine models.
Parallel and distributed architectures the need for parallel and distributed computation parallel computing systems and their classification. Fox algorithm of matrix multiplication in case of checkerboard data decomposition 7. Pdf parallel algorithms for matrix multiplication researchgate. Parallel algorithms for dense linear algebra computations. Parallelism in matrix computations request pdf researchgate. The second part covers dataintensive algorithms for information retrieval and datamining problems and will focus on spark, the new open source framework for in memory bigdata computations, which includes also an. These notes attempt to provide a short guided tour of some of the new concepts at a.
The design of parallel algorithms and data structures, or even the design of existing algorithms and data structures for parallelism, require new paradigms and techniques. We conclude this chapter by presenting four examples of parallel algorithms. This is a valuable reference book for researchers and practitioners in parallel computing. Each chapter is devoted to some aspects of the subject. Cannons algorithm of matrixmatrix multiplication 6 goal. In the parallel algorithm using pprocessors, these weights can be used for choosing ppairs of block columns, which are far from orthogonality with respect to those ksmallest angles. For test the parallel algorithm were used the following number of cores. There is an inherent bound on how fine the granularity of a computation can be. The goal is simply to introduce parallel algorithms and their description in terms of tasks and channels.
Parallelism in matrix computations efstratios gallopoulos springer. This tutorial provides an introduction to the design and analysis of. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including 1 direct solution of dense, structured, or sparse linear systems, 2 dense or structured least squares computations, 3 dense or structured. Buy parallel algorithms for matrix computations on. Today parallel computers are available as commercial products.1577 638 493 1213 1349 116 632 1004 1246 1047 604 1156 1387 874 833 1224 452 1456 1279 357 894 524 609 134 1554 1262 1413 100 1433 1151 93 1183 1277 926 715 591 346 204 457 1499 1036 9 1212 1107 394