Download or read book Numerical Linear Algebra written by Holger Wendland and published by Cambridge University Press. This book was released on 2018 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
Download or read book Numerical Linear Algebra written by Holger Wendland and published by Cambridge University Press. This book was released on 2017-11-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
Download or read book Introduction to Numerical Linear Algebra and Optimisation written by Philippe G. Ciarlet and published by Cambridge University Press. This book was released on 1989-08-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a thorough introduction to the most commonly used methods of numerical linear algebra and optimisation. The prerequisites are some familiarity with the basic properties of matrices, finite-dimensional vector spaces, advanced calculus, and some elementary notations from functional analysis. The book is in two parts. The first deals with numerical linear algebra (review of matrix theory, direct and iterative methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimisation (general algorithms, linear and nonlinear programming). The author has based the book on courses taught for advanced undergraduate and beginning graduate students and the result is a well-organised and lucid exposition. Summaries of basic mathematics are provided, proofs of theorems are complete yet kept as simple as possible, and applications from physics and mechanics are discussed. Professor Ciarlet has also helpfully provided over 40 line diagrams, a great many applications, and a useful guide to further reading. This excellent textbook, which is translated and revised from the very successful French edition, will be of great value to students of numerical analysis, applied mathematics and engineering.
Download or read book Applied Numerical Linear Algebra written by James W. Demmel and published by SIAM. This book was released on 1997-08-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Download or read book Numerical Algebra Matrix Theory Differential Algebraic Equations and Control Theory written by Peter Benner and published by Springer. This book was released on 2015-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Download or read book Numerical Polynomial Algebra written by Hans J. Stetter and published by SIAM. This book was released on 2004-05-01 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive treatment of numerical polynomial algebra, an area which so far has received little attention.
Download or read book Numerical Linear Algebra with Applications written by William Ford and published by Academic Press. This book was released on 2014-09-14 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Linear Algebra with Applications is designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, using MATLAB as the vehicle for computation. The book contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. The text consists of six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra. It explains in great detail the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra. In addition to examples from engineering and science applications, proofs of required results are provided without leaving out critical details. The Preface suggests ways in which the book can be used with or without an intensive study of proofs. This book will be a useful reference for graduate or advanced undergraduate students in engineering, science, and mathematics. It will also appeal to professionals in engineering and science, such as practicing engineers who want to see how numerical linear algebra problems can be solved using a programming language such as MATLAB, MAPLE, or Mathematica. - Six introductory chapters that thoroughly provide the required background for those who have not taken a course in applied or theoretical linear algebra - Detailed explanations and examples - A through discussion of the algorithms necessary for the accurate computation of the solution to the most frequently occurring problems in numerical linear algebra - Examples from engineering and science applications
Download or read book Numerical Linear Algebra and Applications written by Biswa Nath Datta and published by SIAM. This book was released on 2010-01-01 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Linear Algebra and Matrix Factorizations written by Tom Lyche and published by Springer Nature. This book was released on 2020-03-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Download or read book Numerical Linear Algebra written by Lloyd N. Trefethen and published by SIAM. This book was released on 2022-06-17 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its original appearance in 1997, Numerical Linear Algebra has been a leading textbook in its field, used in universities around the world. It is noted for its 40 lecture-sized short chapters and its clear and inviting style. It is reissued here with a new foreword by James Nagy and a new afterword by Yuji Nakatsukasa about subsequent developments.
Download or read book Numerical Linear Algebra for Applications in Statistics written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Linear Algebra Theory and Applications written by Larisa Beilina and published by Springer. This book was released on 2017-09-19 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigenproblems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.
Download or read book Numerical Linear Algebra written by Folkmar Bornemann and published by Springer. This book was released on 2018-01-29 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the algorithmic-numerical thinking using basic problems of linear algebra. By focusing on linear algebra, it ensures a stronger thematic coherence than is otherwise found in introductory lectures on numerics. The book highlights the usefulness of matrix partitioning compared to a component view, leading not only to a clearer notation and shorter algorithms, but also to significant runtime gains in modern computer architectures. The algorithms and accompanying numerical examples are given in the programming environment MATLAB, and additionally – in an appendix – in the future-oriented, freely accessible programming language Julia. This book is suitable for a two-hour lecture on numerical linear algebra from the second semester of a bachelor's degree in mathematics.
Download or read book Numerical Linear Algebra in Signals Systems and Control written by Paul Van Dooren and published by Springer Science & Business Media. This book was released on 2011-05-21 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of Numerical Linear Algebra in Signals, Systems and Control is to present an interdisciplinary book, blending linear and numerical linear algebra with three major areas of electrical engineering: Signal and Image Processing, and Control Systems and Circuit Theory. Numerical Linear Algebra in Signals, Systems and Control will contain articles, both the state-of-the-art surveys and technical papers, on theory, computations, and applications addressing significant new developments in these areas. The goal of the volume is to provide authoritative and accessible accounts of the fast-paced developments in computational mathematics, scientific computing, and computational engineering methods, applications, and algorithms. The state-of-the-art surveys will benefit, in particular, beginning researchers, graduate students, and those contemplating to start a new direction of research in these areas. A more general goal is to foster effective communications and exchange of information between various scientific and engineering communities with mutual interests in concepts, computations, and workable, reliable practices.
Download or read book Applied Numerical Linear Algebra written by William W. Hager and published by SIAM. This book was released on 2022-01-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces numerical issues that arise in linear algebra and its applications. It touches on a wide range of techniques, including direct and iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Detailed explanations on a wide range of topics from condition numbers to singular value decomposition are provided, as well as material on nonlinear and linear systems. Numerical examples, often based on discretizations of boundary-value problems, are used to illustrate concepts. Exercises with detailed solutions are provided at the end of the book, and supplementary material and updates are available online. This Classics edition is appropriate for junior and senior undergraduate students and beginning graduate students in courses such as advanced numerical analysis, special topics on numerical analysis, topics on data science, topics on numerical optimization, and topics on approximation theory.
Download or read book Numerical Linear Algebra with Julia written by Eric Darve and published by SIAM. This book was released on 2021-09-02 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve linear systems using iterative methods such as conjugate gradient. Julia code is provided to illustrate concepts and allow readers to explore methods on their own. Written in a friendly and approachable style, the book contains detailed descriptions of algorithms along with illustrations and graphics that emphasize core concepts and demonstrate the algorithms. Numerical Linear Algebra with Julia is a textbook for advanced undergraduate and graduate students in most STEM fields and is appropriate for courses in numerical linear algebra. It may also serve as a reference for researchers in various fields who depend on numerical solvers in linear algebra.
Download or read book Differential algebraic Equations written by Peter Kunkel and published by European Mathematical Society. This book was released on 2006 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-algebraic equations are a widely accepted tool for the modeling and simulation of constrained dynamical systems in numerous applications, such as mechanical multibody systems, electrical circuit simulation, chemical engineering, control theory, fluid dynamics and many others. This is the first comprehensive textbook that provides a systematic and detailed analysis of initial and boundary value problems for differential-algebraic equations. The analysis is developed from the theory of linear constant coefficient systems via linear variable coefficient systems to general nonlinear systems. Further sections on control problems, generalized inverses of differential-algebraic operators, generalized solutions, and differential equations on manifolds complement the theoretical treatment of initial value problems. Two major classes of numerical methods for differential-algebraic equations (Runge-Kutta and BDF methods) are discussed and analyzed with respect to convergence and order. A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods. A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics, engineering and sciences, as well as practitioners in industry. A prerequisite is a standard course on the numerical solution of ordinary differential equations. Numerous examples and exercises make the book suitable as a course textbook or for self-study.
