Numerical Methods for Laplace Transform Inversion

Author: Alan M. Cohen
Publisher: Springer Science & Business Media
ISBN: 0387688552
Format: PDF, ePub
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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.

2014 International Conference on Mechanical Engineering and Automation ICMEA2014

Author:
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.

The Laplace Transform

Author: Richard Bellman
Publisher: World Scientific
ISBN: 9789971966737
Format: PDF, Mobi
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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.

Complex Variables and the Laplace Transform for Engineers

Author: Wilbur R. LePage
Publisher: Courier Corporation
ISBN: 0486136442
Format: PDF, Docs
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Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.

Computational Aspects of Linear Control

Author: Claude Brezinski
Publisher: Springer Science & Business Media
ISBN: 9781402007118
Format: PDF, ePub, Docs
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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.

Computational Probability

Author: Winfried K. Grassmann
Publisher: Springer Science & Business Media
ISBN: 9780792386179
Format: PDF, ePub, Docs
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Great advances have been made in recent years in the field of computational probability. In particular, the state of the art - as it relates to queuing systems, stochastic Petri-nets and systems dealing with reliability - has benefited significantly from these advances. The objective of this book is to make these topics accessible to researchers, graduate students, and practitioners. Great care was taken to make the exposition as clear as possible. Every line in the book has been evaluated, and changes have been made whenever it was felt that the initial exposition was not clear enough for the intended readership. The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail: Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.

Numerical Methods for Large Eigenvalue Problems

Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Format: PDF
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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.