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Invariant Imbedding

Proceedings of the Summer Workshop on Invariant Imbedding held at the University of Southern California, June – August 1970

  • Conference proceedings
  • © 1971

Overview

Editors:
  1. R. E. Bellman

    1. University of Southern California, Los Angeles, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. E. D. Denman

    1. University of Houston, Houston, USA

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Economics and Mathematical Systems (LNE, volume 52)

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Table of contents (9 papers)

  1. Front Matter

    Pages i-3
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  2. Invariant Imbedding and Linear Systems

    • Eugene D. Denman
    Pages 4-18

  3. Cauchy Problems for Ordinary Differential, Difference and Integral Equations

    • Edward S. Angel
    Pages 19-33

  4. Invariant Imbedding and Partial Differential Equations

    • Edward S. Angel, A. Jain
    Pages 34-45

  5. Reduction of Matrix Integral Equations with Displacement Kernels on the Half-Line to Cauchy Systems

    • Robert E. Kalaba
    Pages 46-54

  6. Invariant Imbedding and Optimal Control

    • Eugene D. Denman
    Pages 55-67

  7. A Method of Characteristics and Invariant Imbedding for Distributed Control Problems

    • Anil K. Jain, Gerald H. Cohen
    Pages 68-86

  8. Wave Propagation through Longitudinally and Transversally Inhomogeneous Slabs-I

    • Ralph Wilcox
    Pages 87-107

  9. Neutron Transport Theory

    • John O. Mingle
    Pages 108-117

  10. Dynamic Programming and Invariant Imbedding in Structural Mechanics

    • Néstor Distéfano
    Pages 118-148

  11. Back Matter

    Pages 149-153
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Keywords

About this book

Imbedding is a powerful and versatile tool for problem­ solving. Rather than treat a question in isolation, we view it as a member of a family of related problems. Each member then becomes a stepping stone in a path to a simultaneous solution of the entire set of problems. As might be expected, there are many ways of accomplishing this imbedding. Time and space variables have been widely employed in the past, while modern approaches combine these structural features with others less immediate. Why should one search for alternate imbeddings when elegant classical formalisms already exist? There are many reasons. To begin with, different imbeddings are useful for different purposes. Some are well suited to the derivation of existence and uniqueness theorems, some to the derivation of conservation relations, some to perturbation techniques and sensitivity analysis, some to computa­ tional studies. The digital computer is designed for initial value problems; the analog computer for boundary-value problems. It is essential then to be flexible and possess the ability to use one device or the other, or both. In economics, engineering, biology and physics, some pro­ cesses lend themselves more easily to one type of imbedding rather than another. Thus, for example, stochastic decision processes are well adapted to dynamic programming. In any case, to go hunting in the wilds of the scientific world armed with only one arrow in one's quiver is quite foolhardy.

Editors and Affiliations

  • University of Southern California, Los Angeles, USA

    R. E. Bellman

  • University of Houston, Houston, USA

    E. D. Denman

Bibliographic Information

  • Book Title: Invariant Imbedding

  • Book Subtitle: Proceedings of the Summer Workshop on Invariant Imbedding held at the University of Southern California, June – August 1970

  • Editors: R. E. Bellman, E. D. Denman

  • Series Title: Lecture Notes in Economics and Mathematical Systems

  • DOI: https://doi.org/10.1007/978-3-642-46274-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin · Heidelberg 1971

  • Softcover ISBN: 978-3-540-05549-5Published: 01 January 1971

  • eBook ISBN: 978-3-642-46274-0Published: 06 December 2012

  • Series ISSN: 0075-8442

  • Series E-ISSN: 2196-9957

  • Edition Number: 1

  • Number of Pages: IV, 150

  • Topics: Operations Research/Decision Theory

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