Download or read book Fast and approximate computation of Laplace and Fourier transforms written by Ines Melzer and published by Logos Verlag Berlin GmbH. This book was released on 2016-03-20 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Fourier Transforms and Approximations written by A M Sedletskii and published by CRC Press. This book was released on 2000-09-20 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three classes of Fourier transforms are presented: Fourier (Laplace) transforms on the halfline, Fourier transforms of measures with compact support and Fourier transforms of rapidly decreasing functions (on whole line). The focus is on the behaviour of Fourier transforms in the region of analyticity and the distribution of their zeros. Applications of results are presented: approximation by exponentials on the finite interval; behavior of the nonharmonic Fourier series; Müntz-Szasz's problem of approximation by powers on unit interval; approximation by weighted exponentials on whole line.
Download or read book Fourier and Laplace Transforms written by and published by Cambridge University Press. This book was released on 2003-08-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.
Download or read book Approximation and Computation A Festschrift in Honor of Walter Gautschi written by R.V.M. Zahar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book An Introduction to Fast Fourier Transform Methods for Partial Differential Equations with Applications written by Morgan Pickering and published by John Wiley & Sons. This book was released on 1986-11-28 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fast Fourier transform (FFT) methods are well established for solving certain types of partial differential equations (PDE). This book is written at an introductory level with the non-specialist user in mind. It first deals with basic ideas and algorithms which may be used to solve problems using simple geometries--the fast Fourier transform is employed and thorough details of the computations are given for a number of illustrative problems. The text proceeds to problems with irregular boundaries, using the capacity matrix approach, and also to more advanced PDE, for which fast solvers may be used as the basis for iterative methods. The use of a numerical Laplace transform technique for certain time-dependent problems is also covered. Throughout the book, the approach is designed to illustrate the essential ideas of the methods employed. References are given for further reading of more advanced or specialized topics.
Download or read book Data Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.
Download or read book Fourier related Transforms Fast Algorithms and Applications written by Okan K. Ersoy and published by Prentice Hall. This book was released on 1997 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting an introduction to all Fourier-related transforms, this work includes a number of applications in the different markets. The accompanying disk provides C and Fortran routines that can be implemented.
Download or read book An Introduction to Laplace Transforms and Fourier Series written by P.P.G. Dyke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Download or read book Fast Fourier Transforms written by James S. Walker and published by CRC Press. This book was released on 2017-11-22 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of an indispensable text provides a clear treatment of Fourier Series, Fourier Transforms, and FFTs. The unique software, included with the book and newly updated for this edition, allows the reader to generate, firsthand, images of all aspects of Fourier analysis described in the text. Topics covered include :
Download or read book Computational Frameworks for the Fast Fourier Transform written by Charles Van Loan and published by SIAM. This book was released on 1992-01-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most comprehensive treatment of FFTs to date. Van Loan captures the interplay between mathematics and the design of effective numerical algorithms--a critical connection as more advanced machines become available. A stylized Matlab notation, which is familiar to those engaged in high-performance computing, is used. The Fast Fourier Transform (FFT) family of algorithms has revolutionized many areas of scientific computation. The FFT is one of the most widely used algorithms in science and engineering, with applications in almost every discipline. This volume is essential for professionals interested in linear algebra as well as those working with numerical methods. The FFT is also a great vehicle for teaching key aspects of scientific computing.
Download or read book Fourier and Laplace Transforms written by Peter David Robinson and published by . This book was released on 1968 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Fourier Transform and Its Applications written by Ronald Newbold Bracewell and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Laplace Transformation I General Theory written by and published by Bookboon. This book was released on with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation and Computation of Fourier Transforms written by Bernhard Walter Romberg and published by . This book was released on 1956 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Computational Methods for Integration written by Prem K. Kythe and published by CRC Press. This book was released on 2004-12-20 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-
Download or read book Radiative Transfer Using Boltzmann Transport Theory written by Carnell Littlejohn and published by Universal-Publishers. This book was released on 2004-12-16 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Radiative transfer of photons though a random distribution of scatterers is considered. The Boltzmann transport eq is used to develop a program to obtain real values of intensity based on a set of discrete time intervals. A Newton-Raphson method is used to determine a set of eigenvalues based on the boundary conditions and system geometry. A numerical method due to Lanczos is used to approximately invert a Laplace transform. The algorithm is designed for easy modification to more general problems. PART II: Eigenvalues for the intensity distribution from the one speed Boltzmann transport equation can be computed using an iteration method with the roots and coefficients for the zeros of the Legendre polynomials and the results converge to the known values based on a Newton-Raphson method used in an earlier treatment for a radiative transfer . A spherical harmonic expansion of the intensity and the application of laplace and finite fourier transforms was used to solve the problem . The zero of a transcendental equation based on the differential equation for the boundary conditions was approximated for the eigenvalues . A Newton-Raphson method was used . Here an iteration method is used with the Legendre polynomials and the results are identical to the Newton-Raphson results therefore the Legendre polynomials can be used to compute the eigenvalues for the intensity distribution . A S16 approximation of the intensity distribution using Fast Fourier Transforms for the coefficients of the interpolating polynomial is given . The program for the coefficients is from a standard Numerical Methods text (Burden and Faires, 1993, Chap.8, p. 309). Arctans from the approximation are compared with the Newton-Raphson eigenvalues.
Download or read book Integral Transforms and Their Applications Third Edition written by Lokenath Debnath and published by CRC Press. This book was released on 2014-11-07 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.
