The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue

S. Friedland, J. Nocedal

ISBN 10: 1332974082 / ISBN 13: 9781332974085

Published by Forgotten Books, 2018

About this Item

Print on Demand. This insightful book advances our understanding of inverse eigenvalue problems in the field of computational science, exploring analytically how to solve the equations that underpin them. It considers the case where multiple eigenvalues are given and offers a practical methodology for obtaining quadratically convergent solutions for both distinct and multiple eigenvalue cases. The methods are illustrated with numerical experiments, elucidating their application. This book provides a comprehensive guide to solving inverse eigenvalue problems, describing not only how to find solutions but also the limits of convergence. It is essential reading for researchers and practitioners working on the theoretical and practical aspects of inverse eigenvalue problems. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781332974085_0

Bibliographic Details

• Title: The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1332974082
• ISBN 13: 9781332974085
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

Explore how to find the right parameters for matrices so they match given eigenvalues with fast, reliable methods. This book presents practical algorithms to solve inverse eigenvalue problems, including when eigenvalues are distinct or repeat. It combines formulation, analysis, and numerical experiments to show how quadratic convergence can be achieved and why certain problems are overdetermined or underdetermined in real applications.

The text introduces the core problems, such as adding or scaling parts of a matrix to force it to have specified eigenvalues, and it explains how to adapt methods for various variations found in engineering and science. Readers will see Newton-type strategies, inverse-iteration techniques, and modifications that maintain fast convergence even in challenging cases with multiple eigenvalues. Concrete examples and detailed discussions of convergence help bridge theory and practice.

- Learn the key problem formulations and when classical methods need adjustments
- See how to handle distinct versus multiple eigenvalues in a unified framework
- Understand how to modify approaches to achieve quadratic convergence
- Review numerical experiments that illustrate performance and limits

Ideal for readers of advanced undergraduate and graduate courses in numerical analysis, applied mathematics, and engineering who seek solid, implementation-ready insight into inverse eigenvalue computations.