Invariant Imbedding

R. E. Bellman

ISBN 10: 3540055495 / ISBN 13: 9783540055495

Published by Springer, J.B. Metzler Jan 1971, 1971

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 160 pp. Englisch.

Seller Inventory # 9783540055495

Bibliographic Details

• Title: Invariant Imbedding
• Publisher: Springer, J.B. Metzler Jan 1971
• Publication Date: 1971
• Language: English
• ISBN 10: 3540055495
• ISBN 13: 9783540055495
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 254W x 178H x 9D millimeters 254 millimeters width by 178 millimeters height by 9 millimeters depth
• Weight: 315 grams

About this title

Synopsis

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.