This book offers an introductory and intermediate-level treatment of all the essential ingredients for achieving high performance in numerical computations.

Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.

This IBM® Redbooks® publication focuses on gathering the correct technical information, and laying out simple guidance for optimizing code performance on IBM POWER8® processor-based systems that run the IBM AIX®, IBM i, or Linux operating systems. There is straightforward performance optimization that can be performed with a minimum of effort and without extensive previous experience or in-depth knowledge. The POWER8 processor contains many new and important performance features, such as support for eight hardware threads in each core and support for transactional memory. The POWER8 processor is a strict superset of the IBM POWER7+TM processor, and so all of the performance features of the POWER7+ processor, such as multiple page sizes, also appear in the POWER8 processor. Much of the technical information and guidance for optimizing performance on POWER8 processors that is presented in this guide also applies to POWER7+ and earlier processors, except where the guide explicitly indicates that a feature is new in the POWER8 processor. This guide strives to focus on optimizations that tend to be positive across a broad set of IBM POWER® processor chips and systems. Specific guidance is given for the POWER8 processor; however, the general guidance is applicable to the IBM POWER7+, IBM POWER7®, IBM POWER6®, IBM POWER5, and even to earlier processors. This guide is directed at personnel who are responsible for performing migration and implementation activities on POWER8 processor-based systems. This includes system administrators, system architects, network administrators, information architects, and database administrators (DBAs).

Provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications.

The MATLAB® programming environment is often perceived as a platform suitable for prototyping and modeling but not for "serious" applications. One of the main complaints is that MATLAB is just too slow. Accelerating MATLAB Performance aims to correct this perception by describing multiple ways to greatly improve MATLAB program speed. Packed with thousands of helpful tips, it leaves no stone unturned, discussing every aspect of MATLAB. Ideal for novices and professionals alike, the book describes MATLAB performance in a scale and depth never before published. It takes a comprehensive approach to MATLAB performance, illustrating numerous ways to attain the desired speedup. The book covers MATLAB, CPU, and memory profiling and discusses various tradeoffs in performance tuning. It describes both the application of standard industry techniques in MATLAB, as well as methods that are specific to MATLAB such as using different data types or built-in functions. The book covers MATLAB vectorization, parallelization (implicit and explicit), optimization, memory management, chunking, and caching. It explains MATLAB’s memory model and details how it can be leveraged. It describes the use of GPU, MEX, FPGA, and other forms of compiled code, as well as techniques for speeding up deployed applications. It details specific tips for MATLAB GUI, graphics, and I/O. It also reviews a wide variety of utilities, libraries, and toolboxes that can help to improve performance. Sufficient information is provided to allow readers to immediately apply the suggestions to their own MATLAB programs. Extensive references are also included to allow those who wish to expand the treatment of a particular topic to do so easily. Supported by an active website, and numerous code examples, the book will help readers rapidly attain significant reductions in development costs and program run times.

“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a tri?ing investment of fact. ” Mark Twain, Life on the Mississippi The challenges in succeeding with computational science are numerous and deeply a?ect all disciplines. NSF’s 2006 Blue Ribbon Panel of Simulation-Based 1 Engineering Science (SBES) states ‘researchers and educators [agree]: com- tational and simulation engineering sciences are fundamental to the security and welfare of the United States. . . We must overcome di?culties inherent in multiscale modeling, the development of next-generation algorithms, and the design. . . of dynamic data-driven application systems. . . We must determine better ways to integrate data-intensive computing, visualization, and simulation. - portantly,wemustoverhauloureducationalsystemtofostertheinterdisciplinary study. . . The payo?sformeeting these challengesareprofound. ’The International Conference on Computational Science 2009 (ICCS 2009) explored how com- tational sciences are not only advancing the traditional hard science disciplines, but also stretching beyond, with applications in the arts, humanities, media and all aspects of research. This interdisciplinary conference drew academic and industry leaders from a variety of ?elds, including physics, astronomy, mat- matics,music,digitalmedia,biologyandengineering. Theconferencealsohosted computer and computational scientists who are designing and building the - ber infrastructure necessary for next-generation computing. Discussions focused on innovative ways to collaborate and how computational science is changing the future of research. ICCS 2009: ‘Compute. Discover. Innovate. ’ was hosted by the Center for Computation and Technology at Louisiana State University in Baton Rouge.

Past and current research in computer performance analysis has focused primarily on dedicated parallel machines. However, future applications in the area of high-performance computing will not only use individual parallel systems but a large set of networked resources. This scenario of computational and data Grids is attracting a great deal of attention from both computer and computational scientists. In addition to the inherent complexity of parallel machines, the sharing and transparency of the available resources introduces new challenges on performance analysis, techniques, and systems. In order to meet those challenges, a multi-disciplinary approach to the multi-faceted problems of performance is required. New degrees of freedom will come into play with a direct impact on the performance of Grid computing, including wide-area network performance, quality-of-service (QoS), heterogeneity, and middleware systems, to mention only a few.

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Euro-ParConferenceSeries The European Conference on Parallel Computing (Euro-Par) is an international conference series dedicated to the promotion and advancement of all aspects of parallel and distributed computing. The major themes fall into the categories of hardware, software, algorithms, and applications. This year, new and interesting topicswereintroduced,likePeer-to-PeerComputing,DistributedMultimedia- stems, and Mobile and Ubiquitous Computing. For the ?rst time, we organized a Demo Session showing many challenging applications. The general objective of Euro-Par is to provide a forum promoting the de- lopment of parallel and distributed computing both as an industrial technique and an academic discipline, extending the frontiers of both the state of the art and the state of the practice. The industrial importance of parallel and dist- buted computing is supported this year by a special Industrial Session as well as a vendors’ exhibition. This is particularly important as currently parallel and distributed computing is evolving into a globally important technology; the b- zword Grid Computing clearly expresses this move. In addition, the trend to a - bile world is clearly visible in this year’s Euro-Par. ThemainaudienceforandparticipantsatEuro-Parareresearchersinaca- mic departments, industrial organizations, and government laboratories. Euro- Par aims to become the primary choice of such professionals for the presentation of new results in their speci?c areas. Euro-Par has its own Internet domain with a permanent Web site where the history of the conference series is described: http://www.euro-par.org. The Euro-Par conference series is sponsored by the Association for Computer Machinery (ACM) and the International Federation for Information Processing (IFIP).

This IBM® Redbooks® publication documents and addresses topics to set up a complete infrastructure environment and tune the applications to use an IBM POWER9TM hardware architecture with the technical computing software stack. This publication is driven by a CORAL project solution. It explores, tests, and documents how to implement an IBM High-Performance Computing (HPC) solution on a POWER9 processor-based system by using IBM technical innovations to help solve challenging scientific, technical, and business problems. This book documents the HPC clustering solution with InfiniBand on IBM Power SystemsTM AC922 8335-GTH and 8335-GTX servers with NVIDIA Tesla V100 SXM2 graphics processing units (GPUs) with NVLink, software components, and the IBM SpectrumTM Scale parallel file system. This solution includes recommendations about the components that are used to provide a cohesive clustering environment that includes job scheduling, parallel application tools, scalable file systems, administration tools, and a high-speed interconnect. This book is divided into three parts: Part 1 focuses on the planners of the solution, Part 2 focuses on the administrators, and Part 3 focuses on the developers. This book targets technical professionals (consultants, technical support staff, IT architects, and IT specialists) who are responsible for delivering cost-effective HPC solutions that help uncover insights among clients' data so that they can act to optimize business results, product development, and scientific discoveries.