Invariant Imbedding
Invariant Imbedding

Author: R.E. Bellman

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 157

ISBN-13: 364246274X

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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.

The Bellman Continuum
The Bellman Continuum

Author: Robert S Roth

Publisher: World Scientific

Published: 1987-02-01

Total Pages: 895

ISBN-13: 9814507938

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This volume is a collection of some of the most significant mathematical works of Prof Richard E Bellman. Ten areas of Prof Bellman's mathematical research were selected by his co-workers for this volume. Each chapter starts with an introductory comment on the significance of Bellman's contribution. Some important mathematical theories are put forward and their applications in physics and biology such as the mathematical aspect of chemotherapy and the analysis of biological systems are included in this book.

Introduction to Matrix Analysis
Introduction to Matrix Analysis

Author: Richard Bellman

Publisher: SIAM

Published: 1997-12-01

Total Pages: 431

ISBN-13: 9781611971170

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Long considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices -- symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics. Written in lucid, concise terms, this volume covers all the key aspects of matrix analysis and presents a variety of fundamental methods. Originally published in 1970, this book replaces the first edition previously published by SIAM in the Classics series. Here you will find a basic guide to operations with matrices and the theory of symmetric matrices, plus an understanding of general square matrices, origins of Markov matrices and non-negative matrices in general, minimum- maximum characterization of characteristic roots, Krnoecker products, functions of matrices, and much more. These ideas and methods will serve as powerful analytical tools. In addition, this volume includes exercises of all levels of difficulty and many references to original papers containing further results. The problem sections contain many useful and interesting results that are not easily found elsewhere. A discussion of the theoretical treatment of matrices in the computational solution of ordinary and partial differential equations, as well as important chapters on dynamic programming and stochastic matrices are also included.

Wave Propagation
Wave Propagation

Author: N.D. Bellman

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 382

ISBN-13: 9400952279

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The SCQlldIII of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with . physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They· draw upon widely different sections of mathematics.