It also treats some subjects that appear for the first time in a textbook, like new results on roundoff effects in the Lanczos and conjugate gradient algorithms. This well-done introduction to the area can be strongly recommended. It is competently written by an author who has contributed much to the complete reshaping of this field in the last twenty years. For a course in matrix iterations, this is just the right book. This book differs substantially from other books on iterative methods, including those recently published, in that it concentrates on several principles behind the derivation and analysis of the most important methods and preconditioning techniques.
Individual algorithms serve as examples illustrating the discussed ideas.
Strong emphasis is given to motivation and its relation to problems in other areas of mathematics. The book speaks in clear language about principal problems in the area of iterative methods. It represents a comprehensive introduction to the field and stimulates the interest of the reader. Strakos, Professor, Czech Academy of Sciences, Institute of Computer Science. Anne Greenbaum is an admired authority in the field of iterative methods.