Download or read book Algorithms for Determining Rational Approximations written by Donald Martin WILLS and published by . This book was released on 1967 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Algorithm for Finding Rational Approximations written by H. F. JR. MATTSON and published by . This book was released on 1960 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rational approximation to a function provides a rapid and convenient way to calculate numerical values of the function to within a predetermined error. The question of how to find rational approximations to given functions is considered. Definitions of terms, a precise statement of what the criterion of best fit is, and statements of some classical results are given. Two closely related iterative methods for finding best rational approximations are defined. A proof of convergence of these methods is given for a special case (in which both methods are the (over) same), and these methods are compared with some others. Some results obtained by one of the iterative methods are presented, together with a brief description of the computer program used to obtain them. (Author).
Download or read book Pade and Rational Approximation written by E.B. Safe and published by Elsevier. This book was released on 2013-05-09 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Padé and Rational Approximation: Theory and Applications presents the proceedings of the Conference on Rational Approximation with Emphasis on Applications of Padé Approximants, held in Tampa, Florida on December 15-17, 1976. The contributors focus on the interplay of theory, computation, and physical applications. This book is composed of six parts encompassing 44 chapters. The introductory part discusses the general theory of orthogonal polynomials that is the mathematical basis of Padé approximants and related matters evaluation. This text also examines the connection between approximants on a stepline in the ordinary Padé table and certain continued fractions and the convergence of diagonal Padé approximants to a class of functions with an even number of branch points. The following parts deal with the special functions and continued fractions of Padé approximation and the theory of rational approximations. These parts also investigate the geometric convergence of Chebyshev rational approximation on the half line, the optimal approximation by “Almost Classical interpolation, and the incomplete polynomials approximation. The discussion then shifts to the physical applications and computations of the Padé approximants. The concluding part presents the applications of rational approximation to gun fire control and to the White Sands Missile Range Computer Facility. This part also provides a list of some open problems and conjectures concerning polynomials and rational functions. This book is of great benefit to mathematicians, physicists, and laboratory workers.
Download or read book Rational Approximation and its Applications in Mathematics and Physics written by Jacek Gilewicz and published by Springer. This book was released on 2006-11-15 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Approximation Theory written by Dietrich Braess and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima tion is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly the same time other approaches to nonlinear approximation were also developed. The use of new tools, such as nonlinear functional analysis and topological methods, showed that linearization is not sufficient for a complete treatment of nonlinear families. In particular, the application of global analysis and the consideration of flows on the family of approximating functions intro duced ideas which were previously unknown in approximation theory. These were and still are important in many branches of analysis. On the other hand, methods developed for nonlinear approximation prob lems can often be successfully applied to problems which belong to or arise from linear approximation. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes. The most famous problem of this kind, namely best interpolation by poly nomials, is treated in the appendix of this book.
Download or read book Algorithms for Approximation written by J. C. Mason and published by Oxford University Press, USA. This book was released on 1987 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "approximation" here refers to the approximation of functions and data by simple functions. Emphasizing the development of useful algorithms and practical applications in defense and industry, the papers cover topics such as multivariate interpolation, optimization methods, constrained problems, spline fitting, data modelling, and applications in microwave measurement, isotropic antennas, sound measurement, and digitized contours. Includes a substantial catalog of existing algorithms. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Faster Algorithms Via Approximation Theory written by Sushant Sachdeva and published by . This book was released on 2014-03-28 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms. The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms. Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas.
Download or read book Trends and Applications in Constructive Approximation written by Detlef H. Mache and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.
Download or read book Algorithms for Minimal Degree Polynomial and Rational Approximation written by James Oliver Evans and published by . This book was released on 1972 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation Theory and Approximation Practice Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Download or read book Rational Approximation and Its Applications in Mathematics and Physics written by Jacek Gilewicz and published by Springer. This book was released on 1987 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods of Numerical Approximation written by D. C. Handscomb and published by Elsevier. This book was released on 2014-05-16 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Numerical Approximation is based on lectures delivered at the Summer School held in September 1965, at Oxford University. The book deals with the approximation of functions with one or more variables, through means of more elementary functions. It explains systems to approximate functions, such as trigonometric sums, rational functions, continued fractions, and spline functions. The book also discusses linear approximation including topics such as convergence of polynomial interpolation and the least-squares approximation. The text analyzes Bernstein polynomials, Weierstrass' theorem, and Lagrangian interpolation. The book also gives attention to the Chebyshev least-squares approximation, the Chebyshev series, and the determination of Chebyshev series, under general methods. These general methods are useful when the student wants to investigate practical methods for finding forms of approximations under various situations. One of the lectures concerns the general theory of linear approximation and the existence of a best approximation approach using different theorems. The book also discusses the theory and calculation of the best rational approximations as well as the optimal approximation of linear functionals. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by statisticians and those working with numbers theory.
Download or read book Fast Algorithms for Best Rational Approximations and Their Applications to Digital Filters written by Ali Sazegari and published by . This book was released on 1988 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithms for Approximation written by Armin Iske and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation methods are vital in many challenging applications of computational science and engineering. This is a collection of papers from world experts in a broad variety of relevant applications, including pattern recognition, machine learning, multiscale modelling of fluid flow, metrology, geometric modelling, tomography, signal and image processing. It documents recent theoretical developments which have lead to new trends in approximation, it gives important computational aspects and multidisciplinary applications, thus making it a perfect fit for graduate students and researchers in science and engineering who wish to understand and develop numerical algorithms for the solution of their specific problems. An important feature of the book is that it brings together modern methods from statistics, mathematical modelling and numerical simulation for the solution of relevant problems, with a wide range of inherent scales. Contributions of industrial mathematicians, including representatives from Microsoft and Schlumberger, foster the transfer of the latest approximation methods to real-world applications.
Download or read book Rational Approximation in Systems Engineering written by BULTHEEL and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Rational Approximation of Real Functions written by P. P. Petrushev and published by Cambridge University Press. This book was released on 2011-03-03 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.
Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 desig
