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The Lanczos Method: Evolution and ApplicationThe Lanczos Method: Evolution and Application

Louis Komzsik

Software, Enviroments and Tools 15

"…I recommend this book to anyone who wants to appreciate the often subtle interactions between algorithm research and engineering applications. For the engineer, it comprehensively summarizes 25 years of intellectual development in the understanding of the basic Lanczos algorithm and its many variants. For the numerical analysts, it describes the variety of practical considerations, which are of critical importance in such applications as structural analysis." — Horst Simon, Director, NERSC Division, Berkeley National Laboratory.

"Detailed development of the method and its algorithmic structure, illustrations by industrial grade examples make this book a welcome addition to the literature on this important subject. The book is a valuable reference…" - Barna A. Szabo, Professor of Mechanics, Washington University, St. Louis.

"The Lanczos method is perhaps the least understood numerical technique used on a daily basis by structural analysts. This book illuminates the mysteries of the method and its real-world examples demonstrate its relevance." —Albert Danial, Application Engineer, TRW, Inc.

The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications drawn from the author’s experience. These chapters provide a unique interaction between the numerical algorithms and their engineering applications.


This is a valuable reference for numerical analysts and engineers and can be used as a supplementary or reference text at the graduate level. Readers should be familiar with basic linear algebra and numerical analysis.


Preface; Part I: Evolution. Chapter 1: The classical Lanczos method; Chapter 2: The Lanczos method in exact arithmetic; Chapter 3: The Lanczos method in finite precision; Chapter 4: Block real symmetric Lanczos method; Chapter 5: Block unsymmetric Lanczos method; Part II: Applications. Chapter 6: Industrial implementation of the Lanczos method; Chapter 7: Free undamped vibrations; Chapter 8: Free damped vibrations; Chapter 9: Forced vibration analysis; Chapter 10: Linear systems and the Lanczos method; Closing Remarks; A Brief Biography of Cornelius Lanczos; Bibliography; Index.

2003 / xii + 87 pages / Softcover / ISBN-13: 978-0-898715-37-8 / ISBN-10: 0-89871-537-7 /
List Price $58.00 / SIAM Member Price $40.60 / Order Code SE15
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