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Theory of Eigenvalue Analysis and Orthogonal Systems (2Hr)

M. Nakhla   and   R. Achar

(ISBN 0-9731047-4-0; First Edition: May 1, 2002; Omniz Global Knowledge Corporation)

This multimedia book presents an in-depth coverage of fundamentals of eigenvalue analysis and orthogonal systems. Starting from the basics, it covers various topics such as QR-decomposition, the relationship between the dominant poles and the leading eigenvalues of a given system etc. It also briefly reviews the Padé approximation and why it is ill conditioned.

The topics covered in this book provide a solid foundation for understanding the iterative techniques for computation of dominant eigenvalues, such as Krylov-subspace techniques. The material presented is accompanied with illustrative animations, reinforced with the audio. The book also provides literature reviews, numerous examples, illustrations, and necessary relations/derivations. The book has been developed in an easy-to-understand style and with in-depth coverage.


The material presented is useful for designers, application engineers, CAD tool developers as well as to those interested in understanding the mathematical principles of electrical systems. The book is also useful to the math community where the complex issue of orthogonal systems is presented in the simple-to-understand form, with the help of intense multimedia presentations. This CD based multimedia book contains approximately two hours of intense multimedia presentations.


Modules

  1. Principles of Eigenvalue Analysis and Related Issues

  2. Orthogonal Systems and QR Decomposition

  3. Exam-1; Exam-2

  4. References


I. Principles of Eigenvalue Analysis and Related Issues

1. Eigenvalues and eigenvectors
    * Example
2. Similarity transformation
    * Theorem 1: Diagonalization

    * Example
    * Theorem 2: Computation of eigenvalues

    *  Example
3. Relationship between poles and eigenvalues
4. Classes of model-order reduction algorithms
5. Overview of Padé approximation
6. Limitations of single expansion techniques
7. Why direct Padé is ill-conditioned?
    * Example
8. Exam;       References

Back to Modules;   Back to Top

II. Orthogonal Systems and QR Decomposition

1. Orthogonal Vectors

     * Example
2. Orthonormal Set of Vectors

     * Example
3. Orthogonal Matrices

     * Example
4. Concept of Orthonormalization
5. Gram-Schmidt Process and QR Decomposition
     * Step-1,     Step-2,      Step-3
     * Summary of the Algorithm
     * Classical Gram-Schmidt (CGS)
     * Modified Gram-Schmidt (MGS)
     * Example
6. Exam

7. References

Back to Modules;   Back to Top

III. Exam

This book has two complete exams which are designed to test the level of one's understanding after completing the study. The questions are such that they broadly cover the material taught in the course and are formulated to reinforce the concepts learnt during the study. The solutions, corrected exam and the final marks are provided after the completion of the exam.

Back to Modules;   Back to Top

IV. References

A Comprehensive list of related references in the leading IEEE international journals and conferences is provided.

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Copyright © 2002, Omniz Global Knowledge Corporation. All rights reserved.
Revised: 07/20/2002

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