Linear Algebra for Computational Sciences and Engineering

Author: Ferrante Neri

Publisher: Springer

ISBN: 3319403419

Category: Computers

Page: 464

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This book presents the main concepts of linear algebra from the viewpoint of applied scientists such as computer scientists and engineers, without compromising on mathematical rigor. Based on the idea that computational scientists and engineers need, in both research and professional life, an understanding of theoretical concepts of mathematics in order to be able to propose research advances and innovative solutions, every concept is thoroughly introduced and is accompanied by its informal interpretation. Furthermore, most of the theorems included are first rigorously proved and then shown in practice by a numerical example. When appropriate, topics are presented also by means of pseudocodes, thus highlighting the computer implementation of algebraic theory. It is structured to be accessible to everybody, from students of pure mathematics who are approaching algebra for the first time to researchers and graduate students in applied sciences who need a theoretical manual of algebra to successfully perform their research. Most importantly, this book is designed to be ideal for both theoretical and practical minds and to offer to both alternative and complementary perspectives to study and understand linear algebra.

Computational Science and Engineering

Author: Gilbert Strang

Publisher: Wellesley-Cambridge Press

ISBN: 9780961408817

Category: Computers

Page: 750

View: 5892

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Encompasses the full range of computational science and engineering from modelling to solution, both analytical and numerical. It develops a framework for the equations and numerical methods of applied mathematics. Gilbert Strang has taught this material to thousands of engineers and scientists (and many more on MIT's OpenCourseWare 18.085-6). His experience is seen in his clear explanations, wide range of examples, and teaching method. The book is solution-based and not formula-based: it integrates analysis and algorithms and MATLAB codes to explain each topic as effectively as possible. The topics include applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis and optimization. This book also serves as a reference for the whole community of computational scientists and engineers. Supporting resources, including MATLAB codes, problem solutions and video lectures from Gilbert Strang's 18.085 courses at MIT, are provided at math.mit.edu/cse.

Lineare Algebra

Author: Gilbert Strang

Publisher: Springer-Verlag

ISBN: 3642556310

Category: Mathematics

Page: 656

View: 8263

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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Wissenschaftliches Rechnen mit MATLAB

Author: Alfio Quarteroni,Fausto Saleri

Publisher: Springer-Verlag

ISBN: 3540293078

Category: Mathematics

Page: 269

View: 8773

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Aus den Rezensionen der englischen Auflage: Dieses Lehrbuch ist eine Einführung in das Wissenschaftliche Rechnen und diskutiert Algorithmen und deren mathematischen Hintergrund. Angesprochen werden im Detail nichtlineare Gleichungen, Approximationsverfahren, numerische Integration und Differentiation, numerische Lineare Algebra, gewöhnliche Differentialgleichungen und Randwertprobleme. Zu den einzelnen Themen werden viele Beispiele und Übungsaufgaben sowie deren Lösung präsentiert, die durchweg in MATLAB formuliert sind. Der Leser findet daher nicht nur die graue Theorie sondern auch deren Umsetzung in numerischen, in MATLAB formulierten Code. MATLAB select 2003, Issue 2, p. 50. [Die Autoren] haben ein ausgezeichnetes Werk vorgelegt, das MATLAB vorstellt und eine sehr nützliche Sammlung von MATLAB Funktionen für die Lösung fortgeschrittener mathematischer und naturwissenschaftlicher Probleme bietet. [...] Die Präsentation des Stoffs ist durchgängig gut und leicht verständlich und beinhaltet Lösungen für die Übungen am Ende jedes Kapitels. Als exzellenter Neuzugang für Universitätsbibliotheken- und Buchhandlungen wird dieses Buch sowohl beim Selbststudium als auch als Ergänzung zu anderen MATLAB-basierten Büchern von großem Nutzen sein. Alles in allem: Sehr empfehlenswert. Für Studenten im Erstsemester wie für Experten gleichermassen. S.T. Karris, University of California, Berkeley, Choice 2003.

Parallel Computing: Accelerating Computational Science and Engineering (CSE)

Author: M. Bader,A. Bode,H.-J. Bungartz

Publisher: IOS Press

ISBN: 1614993815

Category: Computers

Page: 872

View: 5765

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Parallel computing has been the enabling technology of high-end machines for many years. Now, it has finally become the ubiquitous key to the efficient use of any kind of multi-processor computer architecture, from smart phones, tablets, embedded systems and cloud computing up to exascale computers. _x000D_ This book presents the proceedings of ParCo2013 – the latest edition of the biennial International Conference on Parallel Computing – held from 10 to 13 September 2013, in Garching, Germany. The conference focused on several key parallel computing areas. Themes included parallel programming models for multi- and manycore CPUs, GPUs, FPGAs and heterogeneous platforms, the performance engineering processes that must be adapted to efficiently use these new and innovative platforms, novel numerical algorithms and approaches to large-scale simulations of problems in science and engineering._x000D_ The conference programme also included twelve mini-symposia (including an industry session and a special PhD Symposium), which comprehensively represented and intensified the discussion of current hot topics in high performance and parallel computing. These special sessions covered large-scale supercomputing, novel challenges arising from parallel architectures (multi-/manycore, heterogeneous platforms, FPGAs), multi-level algorithms as well as multi-scale, multi-physics and multi-dimensional problems._x000D_ It is clear that parallel computing – including the processing of large data sets (“Big Data”) – will remain a persistent driver of research in all fields of innovative computing, which makes this book relevant to all those with an interest in this field.

Applications of Geometric Algebra in Computer Science and Engineering

Author: Leo Dorst,Chris Doran,Joan Lasenby

Publisher: Springer Science & Business Media

ISBN: 9780817642679

Category: Mathematics

Page: 478

View: 7377

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Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Computational Matrix Analysis

Author: Alan J. Laub

Publisher: SIAM

ISBN: 1611972205

Category: Mathematics

Page: 170

View: 6139

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This text provides an introduction to numerical linear algebra together with its application to solving problems arising in state-space control and systems theory. The book provides a number of elements designed to help the reader learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis and an introduction to finite (IEEE) arithmetic, alongside discussion of mathematical software topics. In addition to the fundamental concepts, the text covers statistical condition estimation and gives an overview of certain computational problems in control and systems theory. Engineers and scientists will find this text valuable as a theoretical resource to complement their work in algorithms. For graduate students beginning their study, or advanced undergraduates, this text is ideal as a one-semester course in numerical linear algebra and is a natural follow-on to the author's previous book, Matrix Analysis for Scientists and Engineers.

Matrix Analysis for Scientists and Engineers

Author: Alan J. Laub

Publisher: SIAM

ISBN: 0898715768

Category: Mathematics

Page: 157

View: 3308

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"Prerequisites for using this text are knowledge of calculus and some previous exposure to matrices and linear algebra, including, for example, a basic knowledge of determinants, singularity of matrices, eigenvalues and eigenvectors, and positive definite matrices. There are exercises at the end of each chapter."--BOOK JACKET.

High Performance Computing for Computational Science - VECPAR 2008

8th International Conference, Toulouse, France, June 24-27, 2008. Revised Selected Papers

Author: José M. Laginha M. Palma,Patrick Amestoy,Michel Daydé,Marta Mattoso,Joao Correira Lopes

Publisher: Springer Science & Business Media

ISBN: 3540928588

Category: Computers

Page: 596

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VECPAR is an international conference series dedicated to the promotion and advancement of all aspects of high-performance computing for computational science, as an industrial technique and academic discipline, extending the fr- tier of both the state of the art and the state of practice. The audience and participants of VECPAR are researchers in academic departments, government laboratories and industrial organizations. There is now a permanent website for the conference series inhttp://vecpar.fe.up.pt where the history of the conference is described. The8theditionofVECPARwasorganizedinToulouse(France),June24–27, 2008. It was the third time the conference was celebrated outside Porto after Valencia (Spain) in2004andRio deJaneiro(Brazil)in 2006. Theconferenceprogrammeconsistedof6invitedtalksand53acceptedpapers out of 73 contributions that were initially submitted. The major themes are divided into: – Large-ScaleSimulationsandNumericalAlgorithmsinComputerScienceand Engineering (aerospace, earth, environment, ?nance, geoscience) – Computing in Healthcare and Biosciences – Multiscale and Multiphysics Problems – Cluster Computing and Grid Computing – Data-Centric and High-Productivity Computing – Cooperative Engineering – Problem-Solving Environments – Imaging and Graphics Twoworkshops,inadditiontotutorials,wereorganizedbeforetheconference: HPDGrid 2008—InternationalWorkshoponHigh-PerformanceDataMana- ment in Grid Environments on June 24 and Sparse Days at CERFACS on June 23 and 24. The most signi?cant contributions are made available in the present book, edited after the conference and after a second review of all orally presented papers at VECPAR 2008 and at the workshops.

A Numerical Library in Java for Scientists and Engineers

Author: Hang T. Lau

Publisher: CRC Press

ISBN: 9781584884309

Category: Mathematics

Page: 1088

View: 1370

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At last researchers have an inexpensive library of Java-based numeric procedures for use in scientific computation. The first and only book of its kind, A Numeric Library in Java for Scientists and Engineers is a translation into Java of the library NUMAL (NUMerical procedures in ALgol 60). This groundbreaking text presents procedural descriptions for linear algebra, ordinary and partial differential equations, optimization, parameter estimation, mathematical physics, and other tools that are indispensable to any dynamic research group. The book offers test programs that allow researchers to execute the examples provided; users are free to construct their own tests and apply the numeric procedures to them in order to observe a successful computation or simulate failure. The entry for each procedure is logically presented, with name, usage parameters, and Java code included. This handbook serves as a powerful research tool, enabling the performance of critical computations in Java. It stands as a cost-efficient alternative to expensive commercial software package of procedural components.

Scientific Computing with Python 3

Author: Claus Fuhrer,Jan Erik Solem,Olivier Verdier

Publisher: Packt Publishing Ltd

ISBN: 1786463644

Category: Computers

Page: 332

View: 2794

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An example-rich, comprehensive guide for all of your Python computational needs About This Book Your ultimate resource for getting up and running with Python numerical computations Explore numerical computing and mathematical libraries using Python 3.x code with SciPy and NumPy modules A hands-on guide to implementing mathematics with Python, with complete coverage of all the key concepts Who This Book Is For This book is for anyone who wants to perform numerical and mathematical computations in Python. It is especially useful for developers, students, and anyone who wants to use Python for computation. Readers are expected to possess basic a knowledge of scientific computing and mathematics, but no prior experience with Python is needed. What You Will Learn The principal syntactical elements of Python The most important and basic types in Python The essential building blocks of computational mathematics, linear algebra, and related Python objects Plot in Python using matplotlib to create high quality figures and graphics to draw and visualize your results Define and use functions and learn to treat them as objects How and when to correctly apply object-oriented programming for scientific computing in Python Handle exceptions, which are an important part of writing reliable and usable code Two aspects of testing for scientific programming: Manual and Automatic In Detail Python can be used for more than just general-purpose programming. It is a free, open source language and environment that has tremendous potential for use within the domain of scientific computing. This book presents Python in tight connection with mathematical applications and demonstrates how to use various concepts in Python for computing purposes, including examples with the latest version of Python 3. Python is an effective tool to use when coupling scientific computing and mathematics and this book will teach you how to use it for linear algebra, arrays, plotting, iterating, functions, polynomials, and much more. Style and approach This book takes a concept-based approach to the language rather than a systematic introduction. It is a complete Python tutorial and introduces computing principles, using practical examples to and showing you how to correctly implement them in Python. You'll learn to focus on high-level design as well as the intricate details of Python syntax. Rather than providing canned problems to be solved, the exercises have been designed to inspire you to think about your own code and give you real-world insight.

Linear Algebra for Mathematics, Science, and Engineering

Author: Edward M. Landesman,Magnus R. Hestenes

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 551

View: 703

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Presenting the fundamentals of linear algebra, this book progresses from matrix theory to the abstract notions of linear space, and covers eigenvalues and eigenvectors. Applications are shown in each chapter, along with problems and exercises.

Domain Decomposition Methods in Science and Engineering XIX

Author: Yunqing Huang,Ralf Kornhuber,Olof Widlund,Jinchao Xu

Publisher: Springer Science & Business Media

ISBN: 9783642113048

Category: Mathematics

Page: 472

View: 5062

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These are the proceedings of the 19th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linear or nonlinear systems of algebraic equations that arise in various problems in mathematics, computational science, engineering and industry. They are designed for massively parallel computers and take the memory hierarchy of such systems into account. This is essential for approaching peak floating point performance. There is an increasingly well-developed theory which is having a direct impact on the development and improvement of these algorithms.

Matrix Computations

Author: Gene H. Golub,Charles F. Van Loan

Publisher: JHU Press

ISBN: 1421407949

Category: Mathematics

Page: 756

View: 6567

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The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

Geometric Algebra with Applications in Science and Engineering

Author: Eduardo Bayro Corrochano,Garret Sobczyk

Publisher: Springer Science & Business Media

ISBN: 9780817641993

Category: Computers

Page: 592

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This book is addressed to a broad audience of cyberneticists, computer scientists, engineers, applied physicists and applied mathematicians. The book offers several examples to clarify the importance of geometric algebra in signal and image processing, filtering and neural computing, computer vision, robotics and geometric physics. The contributions of this book will help the reader to greater understand the potential of geometric algebra for the design and implementation of real time artifical systems.

Linear Algebra

Author: Jin Ho Kwak,Sungpyo Hong

Publisher: Springer Science & Business Media

ISBN: 9780817642945

Category: Business & Economics

Page: 390

View: 9435

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From a review of the first edition: "A logical development of the subject . . . all the important theorems and results are discussed in terms of simple worked examples. The student's understanding . . . is tested by problems at the end of each subsection, and every chapter ends with exercises." —CURRENT SCIENCE A cornerstone of undergraduate mathematics, science, and engineering, this clear and rigorous presentation of the fundamentals of linear algebra is unique in its emphasis and integration of computational skills and mathematical abstractions. The power and utility of this beautiful subject is demonstrated, in particular, in its focus on linear recurrence, difference and differential equations that affect applications in physics, computer science, and economics. Key topics and features: • Linear equations, matrices, determinants, vector spaces, complex vector spaces, inner products, Jordan canonical forms, and quadratic forms • Rich selection of examples and explanations, as well as a wide range of exercises at the end of every section • Selected answers and hints • Excellent index This second edition includes substantial revisions, new material on minimal polynomials and diagonalization, as well as a variety of new applications. The text will serve theoretical and applied courses and is ideal for self-study. With its important approach to linear algebra as a coherent part of mathematics and as a vital component of the natural and social sciences, Linear Algebra, Second Edition will challenge and benefit a broad audience.

Mathematical Modeling and Simulation

Introduction for Scientists and Engineers

Author: Kai Velten

Publisher: John Wiley & Sons

ISBN: 3527627618

Category: Science

Page: 362

View: 3824

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This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

Numerical Linear Algebra and Applications, Second Edition

Author: Biswa Nath Datta

Publisher: SIAM

ISBN: 0898717655

Category: Algebras, Linear

Page: 530

View: 5869

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Full of features and applications, this acclaimed textbook for upper undergraduate level and graduate level students includes all the major topics of computational linear algebra, including solution of a system of linear equations, least-squares solutions of linear systems, computation of eigenvalues, eigenvectors, and singular value problems. Drawing from numerous disciplines of science and engineering, the author covers a variety of motivating applications. When a physical problem is posed, the scientific and engineering significance of the solution is clearly stated. Each chapter contains a summary of the important concepts developed in that chapter, suggestions for further reading, and numerous exercises, both theoretical and MATLAB and MATCOM based. The author also provides a list of key words for quick reference. The MATLAB toolkit available online, 'MATCOM', contains implementations of the major algorithms in the book and will enable students to study different algorithms for the same problem, comparing efficiency, stability, and accuracy.