Fast And Approximate Computation Of Laplace And Fourier Transforms
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Fast And Approximate Computation Of Laplace And Fourier Transforms
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Author : Ines Melzer
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2016-03-20
Fast And Approximate Computation Of Laplace And Fourier Transforms written by Ines Melzer and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-20 with Mathematics categories.
In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments.
Approximation And Computation A Festschrift In Honor Of Walter Gautschi
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Author : R.V.M. Zahar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Approximation And Computation A Festschrift In Honor Of Walter Gautschi written by R.V.M. Zahar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
R. V. M. Zahar* The sixty-fifth birthday of Walter Gautschi provided an opportune moment for an international symposium in his honor, to recognize his many contributions to mathematics and computer sciences. Conceived by John Rice and sponsored by Purdue University, the conference took place in West Lafayette from December 2 to 5, 1993, and was organized around the four main themes representing Professor Gautschi's principal research interests: Approximation, Orthogonal Polynomials, Quadrature and Special Functions. Thirty-eight speakers - colleagues, co-authors, research collaborators or doctoral students of Professor Gautschi - were invited to present articles at the conference, their lectures providing an approximately equal representation of the four disciplines. Five invited speakers, Germund Dahlquist, Philip Davis, Luigi Gatteschi, Werner Rheinboldt and Stephan Ruscheweyh, were unable to present their talks because of illness or other commitments, although Professors Dahlquist, Gatteschi and Ruscheweyh subsequently contributed arti cles to these proceedings. Thus, the final program contained thirty-three technical lectures, ten of which were plenary sessions. Approximately eighty scientists attended the conference, and for some ses sions - in particular, Walter's presentation of his entertaining and informative Reflections and Recollections - that number was complemented by many visitors and friends, as well as the family of the honoree. A surprise visit by Paul Erdos provided one of the highlights of the conference week. The ambiance at the sym posium was extremely collegial, due no doubt to the common academic interests and the personal friendships shared by the participants.
The Fourier Transform And Its Applications
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Author : Ronald Newbold Bracewell
language : en
Publisher:
Release Date : 1978
The Fourier Transform And Its Applications written by Ronald Newbold Bracewell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Fourier transformations categories.
Fundamentals Of Classical Fourier Analysis
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Author : Shashank Tiwari
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Fundamentals Of Classical Fourier Analysis written by Shashank Tiwari and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Fundamentals of Classical Fourier Analysis" is a comprehensive guide to understanding fundamental concepts, techniques, and applications of Fourier analysis in classical mathematics. This book provides a thorough exploration of Fourier analysis, from its historical origins to modern-day applications, offering readers a solid foundation in this essential area of mathematics. Classical Fourier analysis has been a cornerstone of mathematics and engineering for centuries, playing a vital role in solving problems in fields like signal processing, differential equations, and quantum mechanics. We delve into the rich history of Fourier analysis, tracing its development from Joseph Fourier's groundbreaking work to modern digital signal processing applications. Starting with an overview of fundamental concepts and motivations behind Fourier analysis, we introduce Fourier series and transforms, exploring their properties, convergence, and applications. We discuss periodic and non-periodic functions, convergence phenomena, and important theorems such as Parseval's identity and the Fourier inversion theorem. Throughout the book, we emphasize both theoretical insights and practical applications, providing a balanced understanding of Fourier analysis and its relevance to real-world problems. Topics include harmonic analysis, orthogonal functions, Fourier integrals, and Fourier transforms, with applications in signal processing, data compression, and partial differential equations. Each chapter includes examples, illustrations, and exercises to reinforce key concepts. Historical insights into key mathematicians and scientists' contributions are also provided. Whether you are a student, researcher, or practitioner in mathematics, engineering, or related fields, "Fundamentals of Classical Fourier Analysis" is a comprehensive and accessible resource for mastering Fourier analysis principles and techniques.
Computational Methods For Linear Integral Equations
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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
Computational Methods For Linear Integral Equations written by Prem Kythe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.
The Analytical Theory Of Heat
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Author : Jean-Baptiste-Joseph Fourier
language : en
Publisher:
Release Date : 1878
The Analytical Theory Of Heat written by Jean-Baptiste-Joseph Fourier and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1878 with Heat categories.
Handbook Of Computational Methods For Integration
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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2004-12-20
Handbook Of Computational Methods For Integration written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-20 with Mathematics categories.
During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-
Computational Science And Its Applications Iccsa 2004
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Author : Antonio Laganà
language : en
Publisher: Springer
Release Date : 2004-04-29
Computational Science And Its Applications Iccsa 2004 written by Antonio Laganà and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-29 with Computers categories.
The natural mission of Computational Science is to tackle all sorts of human problems and to work out intelligent automata aimed at alleviating the b- den of working out suitable tools for solving complex problems. For this reason ComputationalScience,thoughoriginatingfromtheneedtosolvethemostch- lenging problems in science and engineering (computational science is the key player in the ?ght to gain fundamental advances in astronomy, biology, che- stry, environmental science, physics and several other scienti?c and engineering disciplines) is increasingly turning its attention to all ?elds of human activity. In all activities, in fact, intensive computation, information handling, kn- ledge synthesis, the use of ad-hoc devices, etc. increasingly need to be exploited and coordinated regardless of the location of both the users and the (various and heterogeneous) computing platforms. As a result the key to understanding the explosive growth of this discipline lies in two adjectives that more and more appropriately refer to Computational Science and its applications: interoperable and ubiquitous. Numerous examples of ubiquitous and interoperable tools and applicationsaregiveninthepresentfourLNCSvolumescontainingthecontri- tions delivered at the 2004 International Conference on Computational Science and its Applications (ICCSA 2004) held in Assisi, Italy, May 14–17, 2004.
Numerical Methods For Laplace Transform Inversion
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Author : Alan M. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-16
Numerical Methods For Laplace Transform Inversion written by Alan M. Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-16 with Mathematics categories.
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.
Integral And Discrete Transforms With Applications And Error Analysis
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Author : Abdul Jerri
language : en
Publisher: CRC Press
Release Date : 2021-11-19
Integral And Discrete Transforms With Applications And Error Analysis written by Abdul Jerri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-19 with Mathematics categories.
This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.