# Search Results for "linear-algebra-for-computational-sciences-and-engineering"

## Linear Algebra for Computational Sciences and Engineering

**Author**: Ferrante Neri**Publisher:**Springer**ISBN:**3319403419**Category:**Computers**Page:**464**View:**9931

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:**4822

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.

## Numerical Methods for General and Structured Eigenvalue Problems

**Author**: Daniel Kressner**Publisher:**Springer Science & Business Media**ISBN:**3540285024**Category:**Mathematics**Page:**258**View:**9053

This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.

## A Short Course in Computational Science and Engineering

*C++, Java and Octave Numerical Programming with Free Software Tools*

**Author**: David Yevick**Publisher:**Cambridge University Press**ISBN:**0521116813**Category:**Computers**Page:**265**View:**6343

"Building on his highly successful textbook on C++, David Yevick provides a concise yet comprehensive one-stop course in three key programming languages, C++, Java and Octave (a freeware alternative to MATLAB). Employing only public-domain software to ensure straightforward implementation for all readers, this book presents a unique overview of numerical and programming techniques relevant to scientific programming, including object-oriented programming, elementary and advanced topics in numerical analysis, physical system modeling, scientific graphics, software engineering and performance issues. Relevant features of each programming language are illustrated with short, incisive examples, and the installation and application of the software is describedin detail. Compact, transparent code in all three programming languages is applied to the fundamental equations of quantum mechanics, electromagnetics, mechanics and statistical mechanics. Uncommented versions of the code that can be immediately modifiedand adapted are provided online for the more involved programs. This compact, practical text is an invaluable introduction for students in all undergraduate- and graduate-level courses in the physical sciences or engineering that require numerical modeling, and also a key reference for instructors and scientific programmers"--

## A Primer on Scientific Programming with Python

**Author**: Hans Petter Langtangen**Publisher:**Springer**ISBN:**3662498871**Category:**Computers**Page:**922**View:**7799

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015

## A First Course on Numerical Methods

**Author**: Uri M. Ascher,Chen Greif**Publisher:**SIAM**ISBN:**0898719984**Category:**Mathematics**Page:**552**View:**1585

Offers students a practical knowledge of modern techniques in scientific computing.

## Graph Algorithms in the Language of Linear Algebra

**Author**: Jeremy Kepner,John Gilbert**Publisher:**SIAM**ISBN:**0898719909**Category:**Mathematics**Page:**375**View:**4935

An introduction to graph algorithms accessible to those without a computer science background.

## A Numerical Library in C for Scientists and Engineers

**Author**: Hang T. Lau**Publisher:**CRC Press**ISBN:**9781420050103**Category:**Mathematics**Page:**816**View:**7060

This extensive library of computer programs-written in C language-allows readers to solve numerical problems in areas of linear algebra, ordinary and partial differential equations, optimization, parameter estimation, and special functions of mathematical physics. The library is based on NUMAL, the program assemblage developed and used at the Centre for Mathematics and Computer Science in Amsterdam, one of the world's leading research centers. The important characteristic of the library is its modular structure. Because it is highly compact, it is well-suited for use on personal computers. The library offers the expert a prodigious collection of procedures for implementing numerical methods. The novice can experiment with the worked examples provided and use the more comprehensive procedures to perform mathematical computations. The library provides a powerful research tool for computer scientists, engineers, and applied mathematicians. Applicable materials can be downloaded from the CRC Press website.

## Elements of Scientific Computing

**Author**: Aslak Tveito,Hans Petter Langtangen,Bjørn Frederik Nielsen,Xing Cai**Publisher:**Springer Science & Business Media**ISBN:**3642112994**Category:**Mathematics**Page:**468**View:**2228

Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.

## Computational Methods for Multiphase Flows in Porous Media

**Author**: Zhangxin Chen,Guanren Huan,Yuanle Ma**Publisher:**SIAM**ISBN:**0898716063**Category:**Computers**Page:**531**View:**1368

This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.

## Introduction to Computational Linear Algebra

**Author**: Nabil Nassif,Jocelyne Erhel,Bernard Philippe**Publisher:**CRC Press**ISBN:**1482258714**Category:**Mathematics**Page:**259**View:**5851

Teach Your Students Both the Mathematics of Numerical Methods and the Art of Computer Programming Introduction to Computational Linear Algebra presents classroom-tested material on computational linear algebra and its application to numerical solutions of partial and ordinary differential equations. The book is designed for senior undergraduate students in mathematics and engineering as well as first-year graduate students in engineering and computational science. The text first introduces BLAS operations of types 1, 2, and 3 adapted to a scientific computer environment, specifically MATLAB®. It next covers the basic mathematical tools needed in numerical linear algebra and discusses classical material on Gauss decompositions as well as LU and Cholesky’s factorizations of matrices. The text then shows how to solve linear least squares problems, provides a detailed numerical treatment of the algebraic eigenvalue problem, and discusses (indirect) iterative methods to solve a system of linear equations. The final chapter illustrates how to solve discretized sparse systems of linear equations. Each chapter ends with exercises and computer projects.

## Scientific Computing with Multicore and Accelerators

**Author**: Jakub Kurzak,David A. Bader,Jack Dongarra**Publisher:**CRC Press**ISBN:**1439825378**Category:**Computers**Page:**514**View:**8200

The hybrid/heterogeneous nature of future microprocessors and large high-performance computing systems will result in a reliance on two major types of components: multicore/manycore central processing units and special purpose hardware/massively parallel accelerators. While these technologies have numerous benefits, they also pose substantial performance challenges for developers, including scalability, software tuning, and programming issues. Researchers at the Forefront Reveal Results from Their Own State-of-the-Art Work Edited by some of the top researchers in the field and with contributions from a variety of international experts, Scientific Computing with Multicore and Accelerators focuses on the architectural design and implementation of multicore and manycore processors and accelerators, including graphics processing units (GPUs) and the Sony Toshiba IBM (STI) Cell Broadband Engine (BE) currently used in the Sony PlayStation 3. The book explains how numerical libraries, such as LAPACK, help solve computational science problems; explores the emerging area of hardware-oriented numerics; and presents the design of a fast Fourier transform (FFT) and a parallel list ranking algorithm for the Cell BE. It covers stencil computations, auto-tuning, optimizations of a computational kernel, sequence alignment and homology, and pairwise computations. The book also evaluates the portability of drug design applications to the Cell BE and illustrates how to successfully exploit the computational capabilities of GPUs for scientific applications. It concludes with chapters on dataflow frameworks, the Charm++ programming model, scan algorithms, and a portable intracore communication framework. Explores the New Computational Landscape of Hybrid Processors By offering insight into the process of constructing and effectively using the technology, this volume provides a thorough and practical introduction to the area of hybrid computing. It discusses introductory concepts and simple examples of parallel computing, logical and performance debugging for parallel computing, and advanced topics and issues related to the use and building of many applications.

## Handbook of Mathematics and Computational Science

**Author**: John W. Harris,Horst Stöcker**Publisher:**Springer Science & Business Media**ISBN:**9780387947464**Category:**Mathematics**Page:**1028**View:**3532

This book gathers thousands of up-to-date equations, formulas, tables, illustrations, and explanations into one invaluable volume. It includes over a thousand pages of mathematical material as well as chapters on probability, mathematical statistics, fuzzy logic, and neural networks. It also contains computer language overviews of C, Fortran, and Pascal.

## The Finite Element Method: Theory, Implementation, and Applications

**Author**: Mats G. Larson,Fredrik Bengzon**Publisher:**Springer Science & Business Media**ISBN:**3642332870**Category:**Computers**Page:**395**View:**5036

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.

## Scientific Computing

*Vol. I - Linear and Nonlinear Equations*

**Author**: John A. Trangenstein**Publisher:**Springer**ISBN:**3319691058**Category:**Mathematics**Page:**622**View:**3420

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

## Computational Matrix Analysis

**Author**: Alan J. Laub**Publisher:**SIAM**ISBN:**1611972205**Category:**Mathematics**Page:**170**View:**8932

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.

## Scientific Computing - An Introduction using Maple and MATLAB

**Author**: Walter Gander,Martin J. Gander,Felix Kwok**Publisher:**Springer Science & Business**ISBN:**3319043250**Category:**Mathematics**Page:**905**View:**8997

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

## Analytical and Computational Methods of Advanced Engineering Mathematics

**Author**: Grant B. Gustafson,Calvin H. Wilcox**Publisher:**Springer Science & Business Media**ISBN:**1461206332**Category:**Mathematics**Page:**733**View:**9811

This book focuses on the topics which provide the foundation for practicing engineering mathematics: ordinary differential equations, vector calculus, linear algebra and partial differential equations. Destined to become the definitive work in the field, the book uses a practical engineering approach based upon solving equations and incorporates computational techniques throughout.

## Geometric Algebra with Applications in Science and Engineering

**Author**: Eduardo Bayro Corrochano,Garret Sobczyk**Publisher:**Springer Science & Business Media**ISBN:**1461201594**Category:**Mathematics**Page:**592**View:**2257

The goal of this book is to present a unified mathematical treatment of diverse problems in mathematics, physics, computer science, and engineer ing using geometric algebra. Geometric algebra was invented by William Kingdon Clifford in 1878 as a unification and generalization of the works of Grassmann and Hamilton, which came more than a quarter of a century before. Whereas the algebras of Clifford and Grassmann are well known in advanced mathematics and physics, they have never made an impact in elementary textbooks where the vector algebra of Gibbs-Heaviside still predominates. The approach to Clifford algebra adopted in most of the ar ticles here was pioneered in the 1960s by David Hestenes. Later, together with Garret Sobczyk, he developed it into a unified language for math ematics and physics. Sobczyk first learned about the power of geometric algebra in classes in electrodynamics and relativity taught by Hestenes at Arizona State University from 1966 to 1967. He still vividly remembers a feeling of disbelief that the fundamental geometric product of vectors could have been left out of his undergraduate mathematics education. Geometric algebra provides a rich, general mathematical framework for the develop ment of multilinear algebra, projective and affine geometry, calculus on a manifold, the representation of Lie groups and Lie algebras, the use of the horosphere and many other areas. This book is addressed to a broad audience of applied mathematicians, physicists, computer scientists, and engineers.

## Introduction to Computational Mathematics

*Second Edition*

**Author**: Xin-She Yang**Publisher:**World Scientific Publishing Company**ISBN:**9814635804**Category:**Mathematics**Page:**344**View:**3690

This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.