Iterative Solution Methods by Owe Axelsson (PDF)

Description

Large linear systems of equations arise in most scientific problems where mathematical models are used. The most efficient methods for solving these equations are iterative methods. The first part of this book contains basic and classical material from the study of linear algebra and numerical linear algebra. The second half of the book is unique among books on this topic, because it is devoted to the construction of preconditioners and iterative acceleration methods of the conjugate gradient type. This book is for graduate students and researchers in numerical analysis and applied mathematics.

User’s Reviews

Editorial Reviews: Review “…the book is the most complete and interesting study of iterative methods for systems of linear equations to date. I strongly recommend it to any researcher in the field or in any other area in which the solution of large systems of linear equations plays an important role…it will become a standard reference in numerical linear algebra…” Joaquim J. Judice, Mathematical Reviews”The author has done a fine job of collecting the plethora of work in this area into an up-to-date, coherent entity….I am sure that this volume is destined to be the bible of iterative methods for many years to come.” T. Hopkins, Computing Reviews”…contains a wealth of relevant mathematical theory which underpins much of the development of this specific but important area of Numerical Linear Algebra. It is likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come.” A. Wathen, The Bulletin of the Institute of Mathematics and its Applications Book Description A valuable resource book for students, tutors and researchers using iterative methods.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book may be attractive to researchers dealing with large linear systems of equations, and hoping to solve these in some quick fashion. Axelsson discusses iterative methods that he claims can converge rapidly. While this may not be generally true, the pragmatic researcher might keep Axelsson’s ideas in mind, and consider applying them to her problems.The first section of the book is somewhat mundane. Totally standard descriptions that can be found in many texts on linear algebra. But the value of the book is in the second section. Where the author offers neat suggestions on how to pick the initial conditions for starting the iterations. As well as a type of steepest gradient descent to speed up the convergence.

⭐For those non-specialists who need to know what iterative methods (Krylov) are, whay they work and how to implement them, this is probably not the best suited book. This book gets deeper and it is clearly written for numerical analysts.

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