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.

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.

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.

This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.

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.

This textbook on numerical methods for linear algebra problems presents detailed explanations that beginning students can read on their own, allowing instructors to go beyond lecturing and making it suitable for a “flipped” classroom. The author covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, and multigrid methods. A detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration is also included, as is a discussion of the use of the SVD for grading. Introduction to Numerical Linear Algebra is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It assumes that the reader has taken a course on linear algebra but reviews background as needed. It is intended as a textbook for a one-semester course on numerical linear algebra and provides background and tools for a range of application areas, including data science.

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.