Hardback : $156.00
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.
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.
Part I. Preliminaries: 1. Introduction; 2. Error, stability and conditioning; Part II. Basic Methods: 3. Direct methods for solving linear systems; 4. Iterative methods for solving linear systems; 5. Calculation of eigenvalues; Part III. Advanced Methods: 6. Methods for large sparse systems; 7. Methods for large dense systems; 8. Preconditioning; 9. Compressed sensing; References; Index.
This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject.
Holger Wendland holds the Chair of Applied and Numerical Analysis at the Universität Bayreuth, Germany. He works in the area of Numerical Analysis and is the author of two books, Scattered Data Approximation (Cambridge, 2005) and Numerische Mathematik (2004, with Robert Schaback).
'Wendland delivers an introductory textbook on numerical linear
algebra intended for advanced undergraduate and graduate students
in applied mathematics. The book covers fairly standard material in
this area; it includes error analysis and ill-conditioning, direct
and iterative methods for the solution of linear systems of
equations, least squares problems, and eigenvalue problems.
Additional advanced topics that are not usually covered in
introductory textbooks include multipole expansions, domain
decomposition methods, and compressive sensing. The book is
generally theoretical and mathematically rigorous in its approach.
Algorithms are given only in pseudocode. … The text will be of
interest primarily to instructors and students in graduate
numerical linear algebra courses.' B. Borchers, Choice
'Wendland's book provides the reader with rigorous and clean proofs
throughout the text. There are a lot of new concepts being
presented that can spark the interest of a student who wishes to
take numerical linear algebra and can also serve as an excellent
resource for an independent study. If you are considering a new
text for your numerical linear algebra class or wish to supplement
with another resource, I would recommend giving this book a
review.' Peter Olszewski, MAA Reviews
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