Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely-used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations. Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in Matlab and are freely available on the Web. Demmel discusses several current research topics, making students aware of both the lively research taking place and connections to other parts of numerical analysis, mathematics, and computer science. Some of this material is developed in questions at the end of each chapter, which are marked Easy, Medium, or Hard according to their difficulty. Some questions are straightforward, supplying proofs of lemmas used in the text. Others are more difficult theoretical or computing problems. Questions involving significant amounts of programming are marked Programming. The computing questions mainly involve Matlab programming, and others involve retrieving, using, and perhaps modifying LAPACK code from NETLIB.
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.
Tackle the Challenges of Parallel Programming in the Visual Effects Industry In Multithreading for Visual Effects, developers from DreamWorks Animation, Pixar, Side Effects, Intel, and AMD share their successes and failures in the messy real-world application area of production software. They provide practical advice on multithreading techniques and visual effects used in popular visual effects libraries (such as Bullet, OpenVDB, and OpenSubdiv), one of the industry’s leading visual effects packages (Houdini), and proprietary animation systems. This information is valuable not just to those in the visual effects arena, but also to developers of high performance software looking to increase performance of their code. Diverse Solutions to Solve Performance Problems After an introductory chapter, each subsequent chapter presents a case study that illustrates how the authors used multithreading techniques to achieve better performance. The authors discuss the problems that occurred and explain how they solved them. The case studies encompass solutions for shaving milliseconds, solutions for optimizing longer running tasks, multithreading techniques for modern CPU architectures, and massive parallelism using GPUs. Some of the case studies include open source projects so you can try out these techniques for yourself and see how well they work.
This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations.Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations. For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language.This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
This book is dedicated to Dr. Benjamin William Remondi for many reasons. The project of writing a Global Positioning System (GPS) book was con ceived in April 1988 at a GPS meeting in Darmstadt, Germany. Dr. Remondi discussed with me the need for an additional GPS textbook and suggested a possible joint effort. In 1989, I was willing to commit myself to such a project. Unfortunately, the timing was less than ideal for Dr. Remondi. Therefore, I decided to start the project with other coauthors. Dr. Remondi agreed and indicated his willingness to be a reviewer. I selected Dr. Herbert Lichtenegger, my colleague from the Technical University Graz, Austria, and Dr. James Collins from Rockville, Maryland, U.S.A. In my opinion, the knowledge of the three authors should cover the wide spectrum of GPS. Dr. Lichtenegger is a geodesist with broad experience in both theory and practice. He has specialized his research to geodetic astron omy including orbital theory and geodynamical phenomena. Since 1986, Dr. Lichtenegger's main interest is dedicated to GPS. Dr. Collins retired from the U.S. National Geodetic Survey in 1980, where he was the Deputy Director. For the past ten years, he has been deeply involved in using GPS technology with an emphasis on surveying. Dr. Collins was the founder and president of Geo/Hydro Inc. My own background is theoretically oriented. My first chief, Prof. Dr. Peter Meissl, was an excellent theoretician; and my former chief, Prof. Dr.mult. Helmut Moritz, fortunately, still is.
Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment Contains an introduction to numerical methods for both ordinary and partial differential equations Concentrates on ordinary differential equations, especially boundary-value problems Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level
This book discusses an integrative approach combining Human Factors expertise with Automotive Engineering. It develops an in-depth case study of designing a fuel-efficient driving intervention and offers an examination of an innovative study of feed-forward eco-driving advice. Assisted Eco-Driving: A Practical Guide to the Design and Testing of an Eco-Driving Assistance System offers an examination of an innovative study of feed-forward eco-driving advice based on current vehicle and road environment status. It presents lessons, insights and utilises a documented scientific and research-led approach to designing novel speed advisory and fuel use minimisation systems suitable for combustion vehicles, hybrids and electric vehicles The audience consists of system designers and those working with interfaces and interactions, UX, human factors and ergonomics and system engineering. Automotive academics, researchers, and practitioners will also find this book of interest.
The world is increasingly concerned with bridging the developmental gap between the developed and developing countries. With the establishment of a number of institutions for funding the projects including the World Bank, Asian Development Bank, and many other agencies, the need to develop mechanisms to assess economically viable projects is more important than ever. The Social-Cost Benefit Analysis (SCBA) is an important technique used in formulating, appraising, and evaluating projects. It is a facet of applied welfare economics which is increasingly being used to identify and assess public projects in both developing and developed countries. This volume presents a comprehensive view of cost-benefit analysis in its theoretical and applied dimensions. Both theory and case studies are presented. The theoretical setting for Cost-Benefit Analysis is established by the first five chapters-"Spatial General Equilibrium and Cost-Benefit Analysis," by David M. Newbery; "Optimum Growth Theory and Social Time Preference: A Computerized Mathematical Modeling Exercise to Choose a Social Discount Rate," by Sardar M. N. Islam; "A Theoretical Inquiry of the Axiomatic Consistency of Distributional Weights used in Cost-Benefit Analysis," by Giuseppe Munda; "The Output Gap: Measurement, Related Concepts, and Policy Implications," by Parameswar Nandakumar; and "A Methodological Comparison of Theoretical Approaches in Dichotomous Choice Contingent Valuation," by John C. Whitehead. This book will be useful as a reference text by professors and students in project appraisal classes and will be of equal value to analysts, planners, and interested general readers.
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o
Accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Regardless of the software system used, the book describes and gives examples of the use of modern computer software for numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, factorisations, matrix and vector norms, and other topics in linear algebra. The book is essentially self- contained, with the topics addressed constituting the essential material for an introductory course in statistical computing. Numerous exercises allow the text to be used for a first course in statistical computing or as supplementary text for various courses that emphasise computations.
There is a need to solve problems in solid and fluid mechanics that currently exceed the resources of current and foreseeable supercomputers. The issue revolves around the number of degrees of freedom of simultaneous equations that one needs to accurately describe the problem, and the computer storage and speed limitations which prohibit such solutions. The goals of tHis symposium were to explore some of the latest work being done in both industry and academia to solve such extremely large problems, and to provide a forum for the discussion and prognostication of necessary future direc tions of both man and machine. As evidenced in this proceedings we believe these goals were met. Contained in this volume are discussions of: iterative solvers, and their application to a variety of problems, e.g. structures, fluid dynamics, and structural acoustics; iterative dynamic substructuring and its use in structural acoustics; the use of the boundary element method both alone and in conjunction with the finite element method; the application of finite difference methods to problems of incompressible, turbulent flow; and algorithms amenable to concurrent computations and their applications. Furthermore, discussions of existing computational shortcomings from the big picture point of view are presented that include recommendations for future work.
It is challenging at best to find a resource that provides the breadth of information necessary to develop a successful micro electro mechanical system (MEMS) design. Micro Electro Mechanical System Design is that resource. It is a comprehensive, single-source guide that explains the design process by illustrating the full range of issues involved,
Structured Parallel Programming offers the simplest way for developers to learn patterns for high-performance parallel programming. Written by parallel computing experts and industry insiders Michael McCool, Arch Robison, and James Reinders, this book explains how to design and implement maintainable and efficient parallel algorithms using a composable, structured, scalable, and machine-independent approach to parallel computing. It presents both theory and practice, and provides detailed concrete examples using multiple programming models. The examples in this book are presented using two of the most popular and cutting edge programming models for parallel programming: Threading Building Blocks, and Cilk Plus. These architecture-independent models enable easy integration into existing applications, preserve investments in existing code, and speed the development of parallel applications. Examples from realistic contexts illustrate patterns and themes in parallel algorithm design that are widely applicable regardless of implementation technology. Software developers, computer programmers, and software architects will find this book extremely helpful. - The patterns-based approach offers structure and insight that developers can apply to a variety of parallel programming models - Develops a composable, structured, scalable, and machine-independent approach to parallel computing - Includes detailed examples in both Cilk Plus and the latest Threading Building Blocks, which support a wide variety of computers
Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises." —Zentrablatt Math ". . . carefully structured with many detailed worked examples . . ." —The Mathematical Gazette ". . . an up-to-date and user-friendly account . . ." —Mathematika An Introduction to Numerical Methods and Analysis addresses the mathematics underlying approximation and scientific computing and successfully explains where approximation methods come from, why they sometimes work (or don't work), and when to use one of the many techniques that are available. Written in a style that emphasizes readability and usefulness for the numerical methods novice, the book begins with basic, elementary material and gradually builds up to more advanced topics. A selection of concepts required for the study of computational mathematics is introduced, and simple approximations using Taylor's Theorem are also treated in some depth. The text includes exercises that run the gamut from simple hand computations, to challenging derivations and minor proofs, to programming exercises. A greater emphasis on applied exercises as well as the cause and effect associated with numerical mathematics is featured throughout the book. An Introduction to Numerical Methods and Analysis is the ideal text for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.
High Performance Parallelism Pearls shows how to leverage parallelism on processors and coprocessors with the same programming – illustrating the most effective ways to better tap the computational potential of systems with Intel Xeon Phi coprocessors and Intel Xeon processors or other multicore processors. The book includes examples of successful programming efforts, drawn from across industries and domains such as chemistry, engineering, and environmental science. Each chapter in this edited work includes detailed explanations of the programming techniques used, while showing high performance results on both Intel Xeon Phi coprocessors and multicore processors. Learn from dozens of new examples and case studies illustrating "success stories" demonstrating not just the features of these powerful systems, but also how to leverage parallelism across these heterogeneous systems. - Promotes consistent standards-based programming, showing in detail how to code for high performance on multicore processors and Intel® Xeon PhiTM - Examples from multiple vertical domains illustrating parallel optimizations to modernize real-world codes - Source code available for download to facilitate further exploration
This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case. - Gives a modern overview of scientific computing including parallel an vector computation - Introduces numerical methods for both ordinary and partial differential equations - Has considerable discussion of both direct and iterative methods for linear systems of equations, including parallel and vector algorithms - Covers most of the main topics for a first course in numerical methods and can serve as a text for this course
All of the published religious works of James I. Wedgwood. Contains: The Larger Meaning of Religion, The Presence of Christ in the Holy Communion, New Insights Into Christian Worship, Meditation for Beginners, The Facts Regarding the Episcopal Succession in the Liberal Catholic Church, The Lambeth Conference and the Validity of Archbishop Mathew's Orders, and The Beginnings of the Liberal Catholic Church.
The coastal ocean comprises the semi-enclosed seas on the continental shelf, including estuaries and extending to the shelf break. This region is the focus of many serious concerns, including coastal inundation by tides, storm surges or sea level change; fisheries and aquaculture management; water quality; harmful algal blooms; planning of facilities (such as power stations); port development and maintenance; and oil spills. This book addresses modeling and simulation of the transport, evolution and fate of particles (physical and biological) in the coastal ocean. It is the first to summarize the state of the art in this field and direct it toward diverse applications, for example in measuring and monitoring sediment motion, oil spills and larval ecology. This is an invaluable textbook and reference work for advanced students and researchers in oceanography, geophysical fluid dynamics, marine and civil engineering, computational science and environmental science.
Game to the Last reveals the story of the men who would become "one of the finest battalions which served in the war", the West Australian 11th Infantry Battalion, AIF, during the gruelling Gallipoli Campaign of 1915. The narrative follows the battalion members as they leave their homes and lives in Western Australia, embark for overseas, experience the excitement and boredom of arid and exotic Egypt, and undergo their baptism of fire in the first wave of the Australian and New Zealand landings at Gallipoli on 25 April 1915.
In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist. Templates, a description of a general algorithm rather than the executable object or source code more commonly found in a conventional software library, offer whatever degree of customization the user may desire. Templates offer three distinct advantages: they are general and reusable; they are not language specific; and they exploit the expertise of both the numerical analyst, who creates a template reflecting in-depth knowledge of a specific numerical technique, and the computational scientist, who then provides "value-added" capability to the general template description, customizing it for specific needs. For each template that is presented, the authors provide: a mathematical description of the flow of algorithm; discussion of convergence and stopping criteria to use in the iteration; suggestions for applying a method to special matrix types; advice for tuning the template; tips on parallel implementations; and hints as to when and why a method is useful.
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