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Author: Timothy A. Davis Publisher: SIAM ISBN: 0898716136 Category : Computers Languages : en Pages : 228
Book Description
The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
Author: Timothy A. Davis Publisher: SIAM ISBN: 0898716136 Category : Computers Languages : en Pages : 228
Book Description
The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.
Author: David Hecker Publisher: CRC Press ISBN: 1351689681 Category : Mathematics Languages : en Pages : 262
Book Description
Linear Methods: A General Education Course is expressly written for non-mathematical students, particularly freshmen taking a required core mathematics course. Rather than covering a hodgepodge of different topics as is typical for a core mathematics course, this text encourages students to explore one particular branch of mathematics, elementary linear algebra, in some depth. The material is presented in an accessible manner, as opposed to a traditional overly rigorous approach. While introducing students to useful topics in linear algebra, the book also includes a gentle introduction to more abstract facets of the subject. Many relevant uses of linear algebra in today’s world are illustrated, including applications involving business, economics, elementary graph theory, Markov chains, linear regression and least-squares polynomials, geometric transformations, and elementary physics. The authors have included proofs of various important elementary theorems and properties which provide readers with the reasoning behind these results. Features: Written for a general education core course in introductory mathematics Introduces elementary linear algebra concepts to non-mathematics majors Provides an informal introduction to elementary proofs involving matrices and vectors Includes useful applications from linear algebra related to business, graph theory, regression, and elementary physics Authors Bio: David Hecker is a Professor of Mathematics at Saint Joseph's University in Philadelphia. He received his Ph.D. from Rutgers University and has published several journal articles. He also co-authored several editions of Elementary Linear Algebra with Stephen Andrilli. Stephen Andrilli is a Professor in the Mathematics and Computer Science Department at La Salle University in Philadelphia. He received his Ph.D. from Rutgers University and also co-authored several editions of Elementary Linear Algebra with David Hecker.
Author: Richard Bronson Publisher: Academic Press ISBN: 0080922252 Category : Mathematics Languages : en Pages : 433
Book Description
Matrix Methods: Applied Linear Algebra, Third Edition, as a textbook, provides a unique and comprehensive balance between the theory and computation of matrices. The application of matrices is not just for mathematicians. The use by other disciplines has grown dramatically over the years in response to the rapid changes in technology. Matrix methods is the essence of linear algebra and is what is used to help physical scientists; chemists, physicists, engineers, statisticians, and economists solve real world problems. Applications like Markov chains, graph theory and Leontief Models are placed in early chapters Readability- The prerequisite for most of the material is a firm understanding of algebra New chapters on Linear Programming and Markov Chains Appendix referencing the use of technology, with special emphasis on computer algebra systems (CAS) MATLAB
Author: C. T. Kelley Publisher: SIAM ISBN: 9781611970944 Category : Mathematics Languages : en Pages : 179
Book Description
Linear and nonlinear systems of equations are the basis for many, if not most, of the models of phenomena in science and engineering, and their efficient numerical solution is critical to progress in these areas. This is the first book to be published on nonlinear equations since the mid-1980s. Although it stresses recent developments in this area, such as Newton-Krylov methods, considerable material on linear equations has been incorporated. This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods, incorporation of inexactness and noise into the analysis, new proofs and implementations of Broyden's method, and globalization of inexact Newton methods. Examples, methods, and algorithmic choices are based on applications to infinite dimensional problems such as partial differential equations and integral equations. The analysis and proof techniques are constructed with the infinite dimensional setting in mind and the computational examples and exercises are based on the MATLAB environment.
Author: Jason W. Osborne Publisher: SAGE Publications ISBN: 1506302750 Category : Psychology Languages : en Pages : 489
Book Description
In a conversational tone, Regression & Linear Modeling provides conceptual, user-friendly coverage of the generalized linear model (GLM). Readers will become familiar with applications of ordinary least squares (OLS) regression, binary and multinomial logistic regression, ordinal regression, Poisson regression, and loglinear models. Author Jason W. Osborne returns to certain themes throughout the text, such as testing assumptions, examining data quality, and, where appropriate, nonlinear and non-additive effects modeled within different types of linear models.
Author: Zdzislaw Jackiewicz Publisher: John Wiley & Sons ISBN: 0470522151 Category : Mathematics Languages : en Pages : 500
Book Description
Learn to develop numerical methods for ordinary differential equations General Linear Methods for Ordinary Differential Equations fills a gap in the existing literature by presenting a comprehensive and up-to-date collection of recent advances and developments in the field. This book provides modern coverage of the theory, construction, and implementation of both classical and modern general linear methods for solving ordinary differential equations as they apply to a variety of related areas, including mathematics, applied science, and engineering. The author provides the theoretical foundation for understanding basic concepts and presents a short introduction to ordinary differential equations that encompasses the related concepts of existence and uniqueness theory, stability theory, and stiff differential equations and systems. In addition, a thorough presentation of general linear methods explores relevant subtopics such as pre-consistency, consistency, stage-consistency, zero stability, convergence, order- and stage-order conditions, local discretization error, and linear stability theory. Subsequent chapters feature coverage of: Differential equations and systems Introduction to general linear methods (GLMs) Diagonally implicit multistage integration methods (DIMSIMs) Implementation of DIMSIMs Two-step Runge-Kutta (TSRK) methods Implementation of TSRK methods GLMs with inherent Runge-Kutta stability (IRKS) Implementation of GLMs with IRKS General Linear Methods for Ordinary Differential Equations is an excellent book for courses on numerical ordinary differential equations at the upper-undergraduate and graduate levels. It is also a useful reference for academic and research professionals in the fields of computational and applied mathematics, computational physics, civil and chemical engineering, chemistry, and the life sciences.
Author: Biswa Datta Publisher: Elsevier ISBN: 008053788X Category : Mathematics Languages : en Pages : 736
Book Description
Numerical Methods for Linear Control Systems Design and Analysis is an interdisciplinary textbook aimed at systematic descriptions and implementations of numerically-viable algorithms based on well-established, efficient and stable modern numerical linear techniques for mathematical problems arising in the design and analysis of linear control systems both for the first- and second-order models. Unique coverage of modern mathematical concepts such as parallel computations, second-order systems, and large-scale solutions Background material in linear algebra, numerical linear algebra, and control theory included in text Step-by-step explanations of the algorithms and examples
Author: John D. Pryce Publisher: Courier Corporation ISBN: 0486173631 Category : Mathematics Languages : en Pages : 322
Book Description
Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.
Author: Timothy A. Davis
Author: Timothy A. Davis
Author: Yousef Saad
Author: David Hecker
Author: D. K. Faddeev
Author: Richard Bronson
Author: C. T. Kelley
Author: Jason W. Osborne
Author: Zdzislaw Jackiewicz
Author: Biswa Datta
Author: John D. Pryce