Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.

'Henk van der Vorst is one of the mathematicians who shaped this new area from its beginning until present and he has now published the present book in CUP's series Cambridge Monographs on Applied and Computational Mathematics. … the book will be particularly helpful in introductory university courses on numerical linear algebra. It strikes a neat balance between mathematical rigour and hands-on approaches for practical use and is therefore very well suited for courses with a mixed audience of mathematicians, engineers, and physicists. However, even the practitioner will find many tips and tricks and the more mathematically inclined can use this readable book with its 226 bibliographical items as a starting point to dive deeper into more specialized literature.'

Source: Zeitschrift für Angewandte Mathematik und Physik

‘Anyone interested in numerical analysis and in applied mathematics should read this book. It is absolutely splendid.’

Source: Numerical Algorithms

‘The book is useful and a source of valuable information …’

Source: Zentralblatt für Mathematik

‘This is a beautiful book … Reading and reviewing this book has been a most pleasant experience. I strongly recommend this text to colleagues and students.’

Source: Zeitschrift für Angewandte Mathematik und Mechanik

'… a compact but comprehensive introduction to iterative methods, also taking account of computer methods.'

Source: Mathematika