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Author: E. Stanley Lee
Publisher: Elsevier
ISBN: 1483266753
Category : Mathematics
Languages : en
Pages : 350
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Book Description
Mathematics in Science and Engineering, Volume 41: Quasilinearization and Invariant Imbedding presents a study on the use of two concepts for obtaining numerical solutions of boundary-value problems—quasilinearization and invariant imbedding. This book emphasizes that the invariant imbedding approach reformulates the original boundary-value problem into an initial value problem by introducing new variables or parameters, while the quasilinearization technique represents an iterative approach combined with linear approximations. This volume focuses on analytical aspects that are concerned with actual convergence rates and computational requirements, considering various efficient algorithms that are suited for various types of boundary-value problems. This publication is a good reference for chemical and control engineers and scientists interested in obtaining numerical solutions of boundary-value problems in their particular fields.
Author: E. Stanley Lee
Publisher: Elsevier
ISBN: 1483266753
Category : Mathematics
Languages : en
Pages : 350
Get Book Here
Book Description
Mathematics in Science and Engineering, Volume 41: Quasilinearization and Invariant Imbedding presents a study on the use of two concepts for obtaining numerical solutions of boundary-value problems—quasilinearization and invariant imbedding. This book emphasizes that the invariant imbedding approach reformulates the original boundary-value problem into an initial value problem by introducing new variables or parameters, while the quasilinearization technique represents an iterative approach combined with linear approximations. This volume focuses on analytical aspects that are concerned with actual convergence rates and computational requirements, considering various efficient algorithms that are suited for various types of boundary-value problems. This publication is a good reference for chemical and control engineers and scientists interested in obtaining numerical solutions of boundary-value problems in their particular fields.
Author: R.E. Bellman
Publisher: Springer Science & Business Media
ISBN: 364246274X
Category : Business & Economics
Languages : en
Pages : 157
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Book Description
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.
Author: Akinao Shimizu
Publisher: Academic Press
ISBN: 1483268349
Category : Technology & Engineering
Languages : en
Pages : 195
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Book Description
Application of Invariant Embedding to Reactor Physics describes the application of the method of invariant embedding to radiation shielding and to criticality calculations of atomic reactors. The authors intend to show how this method has been applied to realistic problems, together with the results of applications which will be useful to shielding design. The book is organized into two parts. Part A deals with the reflection and transmission of gamma rays by slabs. The chapters in this section cover topics such as the reflection and transmission problem of gamma rays; formulation of the problem based on the invariant embedding principle; solutions of equations for simplified models; and solving the equations for the reflection and transmission functions based on the realistic cross section for gamma rays. Part B discusses applications to criticality calculations, covering one-dimensional and two-dimensional problems.
Author: Robert S Roth
Publisher: World Scientific
ISBN: 9814507938
Category : Mathematics
Languages : en
Pages : 895
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Book Description
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.
Author: Bellman
Publisher: Academic Press
ISBN: 0080955479
Category : Computers
Languages : en
Pages : 266
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Book Description
This work discusses the theory of control processes. The extremely rapid growth of the theory, associated intimately with the continuing trend toward automation, makes it imperative that the courses of this nature rest upon a broad basis. The work discusses the fundamentals of the calculus of variations, dynamic programming, discrete control processes, use of the digital computer, and functional analysis. Introductory courses in control theory are essential for training the modern graduate student in pure and applied mathematics, engineering, mathematical physics, economics, biology, operations research, and related fields. The work also describes the dual approaches of the calculus of variations and dynamic programming in the scalar case and illustrates ways to tackle the multidimensional optimization problems.
Author:
Publisher: Academic Press
ISBN: 008095619X
Category : Technology & Engineering
Languages : en
Pages : 385
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Book Description
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Author: Richard Bellman
Publisher:
ISBN:
Category : Invariant imbedding
Languages : en
Pages : 368
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Book Description
Author: Zabih Ghassemlooy
Publisher: CRC Press
ISBN: 1498767540
Category : Technology & Engineering
Languages : en
Pages : 590
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Book Description
Visible Light Communications, written by leading researchers, provides a comprehensive overview of theory, stimulation, design, implementation, and applications. The book is divided into two parts – the first devoted to the underlying theoretical concepts of the VLC and the second part covers VLC applications. Visible Light Communications is an emerging topic with multiple functionalities including data communication, indoor localization, 5G wireless communication networks, security, and small cell optimization. This concise book will be of valuable interest from beginners to researchers in the field.
Author: Roel Snieder
Publisher: Cambridge University Press
ISBN: 9780521787512
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Problems based mathematical methods textbook for undergraduates and lower-level graduate students in the physical sciences.
Author: Roel Snieder
Publisher: Cambridge University Press
ISBN: 1107084962
Category : Mathematics
Languages : en
Pages : 583
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Book Description
This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.
