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Books in Numerical analysis

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Interpolation of Operators

  • 1st Edition
  • Volume 129
  • April 1, 1988
  • Colin Bennett + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 4 4 8 - 7
This book presents interpolation theory from its classical roots beginning with Banach function spaces and equimeasurable rearrangements of functions, providing a thorough introduction to the theory of rearrangement-invariant Banach function spaces. At the same time, however, it clearly shows how the theory should be generalized in order to accommodate the more recent and powerful applications. Lebesgue, Lorentz, Zygmund, and Orlicz spaces receive detailed treatment, as do the classical interpolation theorems and their applications in harmonic analysis.The text includes a wide range of techniques and applications, and will serve as an amenable introduction and useful reference to the modern theory of interpolation of operators.

Numerical Modelling: Applications to Marine Systems

  • 1st Edition
  • Volume 145
  • September 1, 1987
  • J. Noye
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 5 6 - 8
The thirteen papers presented in this book are based on talks given at the workshop on Numerical Modelling of Marine Systems held at the University of Adelaide, South Australia in February 1986. Several of the articles are a direct outcome of two special sessions held on modelling of Open Boundary Conditions and on the Transport of Pollutants.Other articles in the book cover topics such as numerical modelling of wind-driven flow in shallow seas, sediment transport in estuaries, internal tides and comparison of numerical methods for solving tidal and pollutant transport problems.

Nonlinear Methods in Numerical Analysis

  • 1st Edition
  • Volume 1
  • March 1, 1987
  • A. Cuyt + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 4 7 - 6
While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.

Mathematical Models and Finite Elements for Reservoir Simulation

  • 1st Edition
  • Volume 17
  • January 1, 1986
  • G. Chavent + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 5 3 8 - 5
Numerical simulators for oil reservoirs have been developed over the last twenty years and are now widely used by oil companies. The research, however, has taken place largely within the industry itself, and has remained somewhat inaccessible to the scientific community. This book hopes to remedy the situation by means of its synthesized presentation of the models used in reservoir simulation, in a form understandable to both mathematicians and engineers.The book aims to initiate a rigorous mathematical study of the immiscible flow models, partly by using the novel `global pressure' approach in treating incompressible two-phase problems. A finite element approximation technique based on the global pressure variational model is presented, and new approaches to the modelling of various kinds of multiphase flow through porous media are introduced.Much of the material is highly original, and has not been presented elsewhere. The mathematical and numerical models should be of great interest to applied mathematicians, and to engineers seeking an alternative approach to reservoir modelling.

Foundations of the Numerical Analysis of Plasticity

  • 1st Edition
  • Volume 107
  • January 1, 1985
  • T. Miyoshi
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 2 1 8 - 6
This monograph describes a theoretical foundation for analysing and developing approximate methods to solve dynamic and quasi-static plasticity problems.

Fast Transforms Algorithms, Analyses, Applications

  • 1st Edition
  • January 28, 1983
  • Douglas F. Elliott + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 1 8 0 6 - 8
This book has grown from notes used by the authors to instruct fast transform classes. One class was sponsored by the Training Department of Rockwell International, and another was sponsored by the Department of Electrical Engineering of The University of Texas at Arlington. Some of the material was also used in a short course sponsored by the University of Southern California. The authors are indebted to their students for motivating the writing of this book and for suggestions to improve it.

Stochastic Models, Estimation, and Control

  • 1st Edition
  • Volume 3
  • August 25, 1982
  • Peter S. Maybeck
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 6 0 0 3 - 6
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.

The Fix-Point Approach to Interdependent Systems

  • 1st Edition
  • Volume 132
  • February 12, 1981
  • H. Wold
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 6 3 0 - 2
Contributions to Economic Analysis, 132: The Fix-Point Approach to Interdependent Systems focuses on the Fix-Point method for the estimation of interdependent systems, including the Algebraic Fix-Point, Parametric Fix-Point, and Parametric Fractional Fix-Point methods. The selection first ponders on the fix-point approach to interdependent systems, iterative algorithms for fix-point estimation, and GEID specification. Discussions focus on the GEID estimator, convergence to multiple parameter sets, design of iterative algorithms, and challenges of simultaneous equations systems. The text then takes a look at the Parametric Fix-Point (PFP) and the Algebraic Fix-Point (AFP) methods; estimation of real-world models by fix-point and other methods; and a search for asymptotically efficient estimators. Topics include autoregressive errors, estimation of the Klein-Goldberger model, estimation of a model of the Czechoslovak economy, and the Parametric Fractional Fix-Point (PFFP) and Parametric Recursive Fix-Point (PRFP) methods. The text elaborates on fix-point estimates of the structure of a model using different Y proxy starts; analysis of the nonlinear Klein-Goldberger model using fix-point estimation and other methods; and fix-point estimation in interdependent systems with specification errors. The selection is a vital reference for researchers interested in the Fix-Point method for the estimation of interdependent systems.

The Finite Element Method for Elliptic Problems

  • 1st Edition
  • Volume 4
  • January 1, 1978
  • P.G. Ciarlet
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 5 2 5 - 5
The objective of this book is to analyze within reasonable limits (it is not a treatise) the basic mathematical aspects of the finite element method. The book should also serve as an introduction to current research on this subject. On the one hand, it is also intended to be a working textbook for advanced courses in Numerical Analysis, as typically taught in graduate courses in American and French universities. For example, it is the author’s experience that a one-semester course (on a three-hour per week basis) can be taught from Chapters 1, 2 and 3 (with the exception of Section 3.3), while another one-semester course can be taught from Chapters 4 and 6. On the other hand, it is hoped that this book will prove to be useful for researchers interested in advanced aspects of the numerical analysis of the finite element method. In this respect, Section 3.3, Chapters 5, 7 and 8, and the sections on “Additional Bibliography and Comments” should provide many suggestions for conducting seminars.

Optimum Design of Digital Control Systemsby Julius T Tou

  • 1st Edition
  • Volume 10
  • January 1, 1963
  • Julius T. Tou
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 5 5 1 7 - 9
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.