Building on this idea, we aim to design linear algebra algorithms and frameworks for hybrid manycore and gpu systems that can enable applications to fully exploit the power that each of the hybrid components offers. Looking back at dense linear algebra software sciencedirect. Atlas stands for automatically tuned linear algebra software. Reduction to hessenberg, tridiagonal, and bidiagonal form. The road to exascale and legacy software for dense linear algebra or what ive been doing for the last 43 years jack dongarra.
Stateoftheart dense linear algebra software, such as the lapack and scalapack libraries, suffers performance losses on multicore processors due to their inability to fully exploit threadlevel parallelism. Jack dongarra specializes in numerical algorithms in linear algebra, parallel computing, the use of advancedcomputer architectures, programming methodology, and tools for parallel computers. With around 20 members, we are one of the largest such groups in the world. A class of parallel tiled linear algebra algorithms for multicore architectures. Dongarra and others published list of freely available software for linear algebra on the web find, read and cite all the. The increasing availability of advancedarchitecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. We will concentrate our e orts on the widely used linear algebra kernels called the basic linear algebra subroutines blas. The current version provides a complete blas api for both c and fortran77, and a very small subset of the lapack. Mathematical software, numerical methods, linear algebra, matrix multiplication, linear equations, eigenvalue problems, vector computer. Linear algebra in particular, the solution of linear systems of equations lies at the heart of most calculations in scientific computing. List of freely available software for linear algebra on the.
Linear algebra software packages encyclopedia of mathematics. He has contributed to the design and implementation of the following open source software packages. Feb 18, 2015 linear algebra in particular, the solution of linear systems of equations lies at the heart of most calculations in scientific computing. Transactions on mathematical software manuscript id toms20170061. In the 1970s, dense linear algebra algorithms were implemented in a systematic way by the linpack project dongarra, bunch, moler and stewart 1979. Parallel linear algebra software for multicore using openmp journal. Scheduling dense linear algebra operations on multicore. Dongarra, linear systems solvers for distributedmemory machines with. This honour recognizes his seminal contributions to algorithms for numerical linear algebra and the design and development of high performance mathematical software.
The original set of fortran basic linear algebra subprograms, or level 1 blas, included vector operations 1. This honour recognizes his seminal contributions to algorithms for numerical linear algebra and the design and development of high performance mathematical software for machines ranging from workstations to. Parallelizing dense and banded linear algebra libraries using smpss. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.
The production of such software for machines ranging from desktop workstations to embedded processors can be a tedious and time consuming process. Numerical linear algebra, particularly the solution of linear systems of equa tions, linear least squares problems, eigenvalue problems and singular value acm transactions on mathematical software, vol. We develop theory, algorithms and software for linear systems, eigenvalue problems, matrix functions, and other problems. Dongarra jj, du croz j, hammarling s, hanson rj 1988 an extended set of fortran basic linear algebra subroutines. Its methods are among the most widely used in applications. It guides you from the very elementary aspects of the subject to the frontiers of current research. Dongarra, du croz, hammarling and du 1990 play important roles as well. Professor jack dongarra has given a detailed comparison of a handful of software packages here. The road to exascale and legacy software for dense linear algebra jack dongarra university of tennessee oak ridge national lab university of manchester. Automatically tuned linear algebra software the netlib. G gustavson, a karpimplementing linear algebra algorithms for. Users of linear algebra may only know some basic operations and concepts, but that does not prevent them from using linear algebra correctly and effectively, thanks to those mathematicians and programmers who wrap the maths into easy to use software. Dongarra, with 4614 highly influential citations and 1436 scientific research papers.
Numerical linear algebra on highperformance computers. The interest is in software for highperformance computers thats available in open source form on the web for solving problems in numerical linear algebra. Linear algebra performs computations associated with matrices, including solutions of linear systems of equations even overdetermined or inconsistent systems and solution by lu factors. Jack dongarra, professor and turing fellow in the school of mathematics and member of the numerical linear algebra group, has been elected as a foreign member of the royal society. Atlas is both a research project and a software package. Dongarra and others published list of freely available software for linear algebra on the web find, read and cite all the research you need on researchgate. Parallel linear algebra software for multicore using openmp. Numerical linear algebra on highperformance computers software, environments and tools 2nd edition by jack j. The design of a parallel dense linear algebra software library.
The objective of the software for linear algebra targeting exascale slate project is to provide fundamental dense linear algebra capabilities to the us department of energy and to the highperformance computing hpc community at large. Solution of least squares and minimum norm problems. This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on highperformance computers. Software for linear algebra targeting exascale slate jack. Dense linear algebra is heavily used throughout the computational sciences. Linear algebra software is software that performs numerical calculations aimed at solving a system of linear equations or related problems such as eigenvalue. Citeseerx automatically tuned linear algebra software. Introduction supercomputing is characterized by its demand for computer systems with high computa tional speed, fast and large main and secondary memory, and the extensive use of parallelism. He specializes in numerical algorithms in linear algebra, parallel computing, the use of advanced computer architectures, programming methodology, and tools for parallel computers. Mathematical software libraries imsl, nag supply subprograms for the. The recent version of the parallel linear algebra software for multicore architectures plasma library is based on tasks with dependencies from the openmp standard. Like euclidean geometry, linear algebra is one of the oldest and most fundamental subjects in mathematics.
This article focuses on some of the recent developments in linear algebra software designed to exploit advancedarchitecture computers over the decades. Software for linear algebra targeting exascale slate project. Software for linear algebra targeting at exascale slate, a numerical linear algebra library. Freely available software for linear algebra the netlib. Distributed tasking for exascale, a run time system parsec. Selfadapting linear algebra algorithms and software. Computers use floatingpoint arithmetic and cannot exactly represent. Hardware and software benchmarking has also been the focus of his professional activities. Automatically tuned linear algebra software proceedings of the.
Slate is to provide fundamental dense linear algebra capabilities for todays highperformance computing hpc community. List of freely available software for linear algebra on the web. His research includes the development, testing and documentation of high quality mathematical software. Linear algebra software for largescale accelerated multicore computing volume 25 a. Software for linear algebra this list contains some of the best linear algebra software. The sun s3l dense linear algebra routines make use of the scalapack library described in scalapack. Fundamental problems in numerical linear algebra are. Selfadapting linear algebra algorithms and software james demmel, fellow, ieee, jack dongarra, fellow, ieee, victor eijkhout, erika fuentes, antoine petitet, richard vuduc, r.
The linear algebra group plans to use algorithms based upon blocking techniques that take advantage of surfacetovolume effects and allow effective reuse of data in local memory. An updated set of basic linear algebra subprograms blas. In addition, he published papers on other matrix factorization scenarios such as parallel outofcore solvers. The objective of the software for linear algebra targeting exascale slate. Linear algebra software for distributed memory architectures, j. Welcome to the website of the numerical linear algebra group in the department of mathematics at the university of manchester. Graph algorithms in the language of linear algebra. Please use any of the following publications to reference magma. Linear algebra in particular, the solution of linear systems of equations lies at the heart of. Clint whaley, and katherine yelick, member, ieee invited paper one of the main obstacles to the ef. Linear algebra software for largescale accelerated. Linear algebra software on a vector computer sciencedirect.
Handbook of linear algebra, second edition leslie hogben. Jul 02, 2019 a talk by jack dongarra at the workshop advances in numerical linear algebra, may 2930, 2019 held in the school of mathematics at the university of manchest. There is hardly a subfield of applied mathematics where linear algebra is not used, though nowadays 1998 its use may be hidden in software. Linear algebra software for largescale accelerated multicore. Hammarling, dongarra, du croz and hanson 1988, and level 3 matrixmatrix operations. A set of level 3 basic linear algebra subprograms acm. Parallel programming models for dense linear algebra on. The road to exascale and legacy software for dense linear. Atlas faq automatically tuned linear algebra software. Jack dongarra on ecpfunded software projects for exascale.
For recent 1998 surveys of algorithms for numerical linear algebra problems, see. A talk by jack dongarra at the workshop advances in numerical linear algebra, may 2930, 2019 held in the school of mathematics at the. Plasma provides implementations of stateoftheart algorithms using cuttingedge task scheduling techniques. This paper proposes adding a set of level 3 blas, which would be used to perform matrixmatrix operations. Citeseerx numerical linear algebra algorithms and software. Automatically tuned linear algebra software project, as well as the fundamental principles that underly it.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Variability of the benchmarked computer architectures and algorithmic approaches was a natural base for his investigation of very broad topic of software selfadaptation. Simon, editors, parallel processing for scientific computing. See chapter 5 for linear algebra done at a higher level. The sustained innovation for linear algebra software silas project updates two of the most widely used numerical libraries in the history of computational science and engineeringlapack and scalapack, abbreviated scalapackenhancing and hardening them for this ongoing revolution in processor architecture and system design.
Atlas is an instantiation of a new paradigm in high. Plasma is a software package for solving problems in dense linear algebra using multicore processors and xeon phi coprocessors. The road to exascale and legacy software for dense linear algebra. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Basic linear algebra subprograms blas is a specification that prescribes a set of lowlevel routines for performing common linear algebra operations such as vector addition, scalar multiplication, dot products, linear combinations, and matrix multiplication. It is a subfield of numerical analysis, and a type of linear algebra. The work described here can help in automating much of this process. His research includes the development, testing and documentation of highquality mathematical software. For a more exhaustive list, or to find materials that fit your specific needs, search or browse linear algebra or software in the forums internet mathematics library.
In this 30 minute live webinar, we will discuss the slate project. Dongarra is also principal investigator on three of the 35 software development proposals funded for the first year of the us department of energys does exascale computing project ecp. With a substantial amount of new material, the handbook of linear algebra, second edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easytouse format. A talk by jack dongarra at the workshop advances in numerical linear algebra, may 2930, 2019 held in the school of mathematics at the university of manchest. List of freely available software for linear algebra on. In addition to the electromagnetics problem we just described, problems from quantum mechanics eigenvalue prob lems, statistics, computational finance and countless other problems are based on dense matrix computations. This approach can lead to optimal algorithms on supercomputers with modest amounts of parallelism, and on distributedmemory machines where the levels of parallelism. Software, environments, and tools jeremy kepner and john gilbert, editors, graph algorithms in the language of linear algebra jeremy kepner, parallel matlab for multicore and multinode computers michael a.
Parallel linear algebra software for multicore using. Software for linear algebra targeting exascale slate. The original basic linear algebra subprograms, now commonly referred to as the blas and fully described in 27, 281, have been very successful, and have been used in a wide range of software including. Piotr luszczek worked on sparse direct methods for matrix factorizations that leveraged existing optimized linear algebra kernel codes.
The main functionality of the library is presented. He holds the position of a distinguished research staff member in the computer science and mathematics division at oak ridge national laboratory, turing fellowship in the school of. Freedom some thoughts on opencontent, intellectual property, opensource software and books. Elements of abstract and linear algebra, by edwin h. Numerical linear algebra for highperformance computers. Atlass purpose is to provide portably optimal linear algebra software.
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