# Download Ebook Free Computational Methods For Modelling Of Nonlinear Systems

## Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett

Publisher : Elsevier

Release Date : 2007-04-11

Category : Mathematics

Total pages :322

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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; and methods 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 particular branches, 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

## Algebraic Linguistics; Analytical Models

Publisher : Unknown

Release Date : 1967

Category : Mathematical linguistics

Total pages :254

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## Advanced Computational Methods in Life System Modeling and Simulation

Publisher : Springer

Release Date : 2017-09-01

Category : Computers

Total pages :609

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The three-volume set CCIS 761, CCIS 762, and CCIS 763 constitutes the thoroughly refereed proceedings of the International Conference on Life System Modeling and Simulation, LSMS 2017, and of the International Conference on Intelligent Computing for Sustainable Energy and Environment, ICSEE 2017, held in Nanjing, China, in September 2017. The 208 revised full papers presented were carefully reviewed and selected from over 625 submissions. The papers of this volume are organized in topical sections on: Biomedical Signal Processing; Computational Methods in Organism Modeling; Medical Apparatus and Clinical Applications; Bionics Control Methods, Algorithms and Apparatus; Modeling and Simulation of Life Systems; Data Driven Analysis; Image and Video Processing; Advanced Fuzzy and Neural Network Theory and Algorithms; Advanced Evolutionary Methods and Applications; Advanced Machine Learning Methods and Applications; Intelligent Modeling, Monitoring, and Control of Complex Nonlinear Systems; Advanced Methods for Networked Systems; Control and Analysis of Transportation Systems; Advanced Sliding Mode Control and Applications; Advanced Analysis of New Materials and Devices; Computational Intelligence in Utilization of Clean and Renewable Energy Resources; Intelligent Methods for Energy Saving and Pollution Reduction; Intelligent Methods in Developing Electric Vehicles, Engines and Equipment; Intelligent Computing and Control in Power Systems; Modeling, Simulation and Control in Smart Grid and Microgrid; Optimization Methods; Computational Methods for Sustainable Environment.

## Computational Solution of Nonlinear Systems of Equations

Publisher : American Mathematical Soc.

Release Date : 1990-04-03

Category : Mathematics

Total pages :762

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Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

## Numerical Methods for Nonlinear Engineering Models

Publisher : Springer Science & Business Media

Release Date : 2009-03-24

Category : Computers

Total pages :1013

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There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

## Numerical Methods for Unconstrained Optimization and Nonlinear Equations

Publisher : SIAM

Release Date : 1996-12-01

Category : Equations

Total pages :378

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This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

## Nonlinear Systems, Vol. 1

Publisher : Springer

Release Date : 2019-10-11

Category :

Total pages :442

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## The Shock and Vibration Digest

Publisher : Unknown

Release Date : 1993

Category : Shock (Mechanics)

Total pages :129

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## Numerical Methods for Nonlinear Partial Differential Equations

Publisher : Springer

Release Date : 2015-01-19

Category : Mathematics

Total pages :393

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The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

## Nonlinear Analysis: Problems, Applications and Computational Methods

Publisher : Springer Nature

Release Date : 2020-11-13

Category : Technology & Engineering

Total pages :249

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This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, time-fractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multi-orthogonal projections and generalized continued fractions. The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.

## Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante

Publisher : Elsevier

Release Date : 1988-05-01

Category : Mathematics

Total pages :322

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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; and methods 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 particular branches, 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

## Advanced Methods of Physiological System Modeling

Publisher : Springer Science & Business Media

Release Date : 2013-06-29

Category : Technology & Engineering

Total pages :272

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This volume is the third in a series entitled" Advanced Methods of Physiological System Modeling" and the fifth in a series of research volumes published by Plenum under the sponsorship of the Biomedical Simulations Resource (BMSR) at the Uni versity of Southern California in the context of dissemination activities supported by the Biomedical Research Technology Program of the National Center for Research Resources at the National Institutes of Health under Grant No. P41 RR-OI861. These volumes are edited by BMSR principal scientists and report on recent research de velopments in the area of physiological systems modeling, as well as on advanced methods for analysis of physiological signals and data. As in the previous two volumes of this series, the work reported herein is con cerned with the development of advanced modeling methodologies and their novel application to problems of biomedical interest, with emphasis on nonlinear aspects of physiological function. The term "advanced methodologies" is used to indicate that the scope of this work extends beyond the ordinary type of analysis, which is confined traditionally to the linear domain. As the importance of nonlinearities in understanding the complex mechanisms of physiological function is increasingly recognized, the need for effective and practical modeling methodologies that address the issue of nonlinear dynamics in life sciences becomes more and more pressing.

## Mathematical Modeling

Publisher : Springer Science & Business Media

Release Date : 2013-03-14

Category : Mathematics

Total pages :294

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This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: • mathematical and computer discrete systems models; • non-linear excitation in condensed media; • complex systems evolution; • mathematical models in economics; • non-equilibrium processes kinematics; • dynamics and structure of the molecular and biomolecular systems; • mathematical transfer models in non-linear systems; • numerical simulation and algorithms; • turbulence and determined chaos; • chemical physics of polymer. This conference was supported by the Russian Ministry of Education, Russian foundation for Basic Research and Federal Program "Integration". This volume contains the following sections: 1. models of non-linear phenomena in physics; 2. numerical methods and computer simulations; 3. mathematical computer models of discrete systems; 4. mathematical models in economics; 5. non-linear models in chemical physics and physical chemistry; 6. mathematical models of transport processes in complex systems. In Sections One and Five a number of fundamental and sufficiently general problems, concerning real physical and physical-chemical systems simulation, is discussed.

## Modelling Mathematical Methods and Scientific Computation

Publisher : CRC Press

Release Date : 1994-12-22

Category : Mathematics

Total pages :512

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Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.

## Adaptive Learning Methods for Nonlinear System Modeling

Publisher : Butterworth-Heinemann

Release Date : 2018-07-05

Category : Technology & Engineering

Total pages :388

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Adaptive Learning Methods for Nonlinear System Modeling presents some of the recent advances on adaptive algorithms and machine learning methods designed for nonlinear system modeling and identification. Real-life problems always entail a certain degree of nonlinearity, which makes linear models a non-optimal choice. This book mainly focuses on those methodologies for nonlinear modeling that involve any adaptive learning approaches to process data coming from an unknown nonlinear system. By learning from available data, such methods aim at estimating the nonlinearity introduced by the unknown system. In particular, the methods presented in this book are based on online learning approaches, which process the data example-by-example and allow to model even complex nonlinearities, e.g., showing time-varying and dynamic behaviors. Possible fields of applications of such algorithms includes distributed sensor networks, wireless communications, channel identification, predictive maintenance, wind prediction, network security, vehicular networks, active noise control, information forensics and security, tracking control in mobile robots, power systems, and nonlinear modeling in big data, among many others. This book serves as a crucial resource for researchers, PhD and post-graduate students working in the areas of machine learning, signal processing, adaptive filtering, nonlinear control, system identification, cooperative systems, computational intelligence. This book may be also of interest to the industry market and practitioners working with a wide variety of nonlinear systems. Presents the key trends and future perspectives in the field of nonlinear signal processing and adaptive learning. Introduces novel solutions and improvements over the state-of-the-art methods in the very exciting area of online and adaptive nonlinear identification. Helps readers understand important methods that are effective in nonlinear system modelling, suggesting the right methodology to address particular issues.