Numerical Methods for Laplace Transform Inversion

Author: Alan M. Cohen
Publisher: Springer Science & Business Media
ISBN: 0387688552
Format: PDF
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This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.

Exponential Data Fitting and Its Applications

Author: Victor Pereyra
Publisher: Bentham Science Publishers
ISBN: 1608050483
Format: PDF, ePub, Docs
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Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision and Robotics. the most commonly used norm in the approximation by linear combinations of exponentials is the l2 norm (sum of squares of residuals), in which case one obtains a nonlinear separable least squares problem. a number of different methods have been proposed through the years to solve these types of problems and new applications appear daily. Necessary guidance is provided so that care should be taken when applying standard or simplified methods to it. the described methods take into account the separability between the linear and nonlinear parameters, which have been quite successful. the accessibility of good, publicly available software that has been very beneficial in many different fields is also considered. This book covers the main solution methods (Variable Projections, Modified Prony) and also emphasizes the applications to different fields. It is considered essential reading for researchers and students in this field.

Computational Methods in Physics

Author: Simon Širca
Publisher: Springer
ISBN: 3319786199
Format: PDF
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This book is intended to help advanced undergraduate, graduate, and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues, as well as optimization of program execution speeds. Numerous examples are given throughout the chapters, followed by comprehensive end-of-chapter problems with a more pronounced physics background, while less stress is given to the explanation of individual algorithms. The readers are encouraged to develop a certain amount of skepticism and scrutiny instead of blindly following readily available commercial tools. The second edition has been enriched by a chapter on inverse problems dealing with the solution of integral equations, inverse Sturm-Liouville problems, as well as retrospective and recovery problems for partial differential equations. The revised text now includes an introduction to sparse matrix methods, the solution of matrix equations, and pseudospectra of matrices; it discusses the sparse Fourier, non-uniform Fourier and discrete wavelet transformations, the basics of non-linear regression and the Kolmogorov-Smirnov test; it demonstrates the key concepts in solving stiff differential equations and the asymptotics of Sturm-Liouville eigenvalues and eigenfunctions. Among other updates, it also presents the techniques of state-space reconstruction, methods to calculate the matrix exponential, generate random permutations and compute stable derivatives.

Computational Aspects of Linear Control

Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 9781402007118
Format: PDF, Kindle
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The main objective of this volume is to create a bridge between control theory and its numerical analysis aspects. It is unique because it presents both subjects in a single volume. The book combines an exposition of linear control theory and the corresponding modern relevant computational techniques such as orthogonal polynomials, Padé approximation, numerical linear algebra, and some topics on nonlinear differential equations. It can be considered as an introduction to control theory for numerical analysts looking for a wide area of applications and as an introduction to recent numerical methods for control specialists. Audience: Aimed at advanced students at a doctoral or post-doctoral level, engineers, and researchers in control theory and numerical analysis.

The Laplace Transform

Author: Richard Bellman
Publisher: World Scientific
ISBN: 9789971966737
Format: PDF, Docs
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The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.

2014 International Conference on Mechanical Engineering and Automation ICMEA2014

Publisher: DEStech Publications, Inc
ISBN: 1605951552
Format: PDF, ePub
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The ICMEA2014 will provide an excellent international academic forum for sharing knowledge and results in theory, methodology and applications of Mechanical Engineering and Automation. The ICMEA2014 is organized by Advanced Information Science Research Center (AISRC) and is co-sponsored by Chongqing University, Changsha University of Science & Technology, Huazong University of Science and Technology and China Three Gorges University. This ICMEA2014 proceedings tends to collect the up-to-date, comprehensive and worldwide state-of-art knowledge on mechanical engineering and automation, including control theory and application, mechanic manufacturing system and automation, and Computer Science and applications. All of accepted papers were subjected to strict peer-reviewing by 2-4 expert referees. The papers have been selected for this volume because of quality and the relevance to the conference. We hope this book will not only provide the readers a broad overview of the latest research results, but also provide the readers a valuable summary and reference in these fields. ICMEA2014 organizing committee would like to express our sincere appreciations to all authors for their contributions to this book. We would like to extend our thanks to all the referees for their constructive comments on all papers; especially, we would like to thank to organizing committee for their hard working.

Introduction to the Laplace Transform

Author: Peter K.F. Kuhfittig
Publisher: Springer Science & Business Media
ISBN: 1489922016
Format: PDF
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The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily. The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.

Numerical Methods for Large Eigenvalue Problems

Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Format: PDF, ePub, Mobi
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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Numerical Algorithms

Author: Justin Solomon
Publisher: CRC Press
ISBN: 1482251892
Format: PDF, Mobi
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Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into the theoretical tools needed to support these skills. The book covers a wide range of topics—from numerical linear algebra to optimization and differential equations—focusing on real-world motivation and unifying themes. It incorporates cases from computer science research and practice, accompanied by highlights from in-depth literature on each subtopic. Comprehensive end-of-chapter exercises encourage critical thinking and build students’ intuition while introducing extensions of the basic material. The text is designed for advanced undergraduate and beginning graduate students in computer science and related fields with experience in calculus and linear algebra. For students with a background in discrete mathematics, the book includes some reminders of relevant continuous mathematical background.

Finite Difference Methods for Ordinary and Partial Differential Equations

Author: Randall J. LeVeque
Publisher: SIAM
ISBN: 9780898717839
Format: PDF, Kindle
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This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.