Topics In Polynomial And Rational Interpolation And Approximation
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Topics In Polynomial And Rational Interpolation And Approximation
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Author : Richard S. Varga
language : en
Publisher:
Release Date : 1982
Topics In Polynomial And Rational Interpolation And Approximation written by Richard S. Varga and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Approximation theory categories.
Interpolation And Approximation By Polynomials
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Author : George M. Phillips
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-04-08
Interpolation And Approximation By Polynomials written by George M. Phillips 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 2003-04-08 with Mathematics categories.
In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Approximation And Optimization
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Author : Juan A. Gomez-Fernandez
language : en
Publisher: Springer
Release Date : 2006-11-14
Approximation And Optimization written by Juan A. Gomez-Fernandez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Scientific Computation On Mathematical Problems And Conjectures
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Author : Richard S. Varga
language : en
Publisher: SIAM
Release Date : 1990-01-01
Scientific Computation On Mathematical Problems And Conjectures written by Richard S. Varga and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-01-01 with Mathematics categories.
Studies the use of scientific computation as a tool in attacking a number of mathematical problems and conjectures. In this case, scientific computation refers primarily to computations that are carried out with a large number of significant digits, for calculations associated with a variety of numerical techniques such as the (second) Remez algorithm in polynomial and rational approximation theory, Richardson extrapolation of sequences of numbers, the accurate finding of zeros of polynomials of large degree, and the numerical approximation of integrals by quadrature techniques. The goal of this book is not to delve into the specialized field dealing with the creation of robust and reliable software needed to implement these high-precision calculations, but rather to emphasize the enormous power that existing software brings to the mathematician's arsenal of weapons for attacking mathematical problems and conjectures. Scientific Computation on Mathematical Problems and Conjectures includes studies of the Bernstein Conjecture of 1913 in polynomial approximation theory, the "1/9" Conjecture of 1977 in rational approximation theory, the famous Riemann Hypothesis of 1859, and the Polya Conjecture of 1927. The emphasis of this monograph rests strongly on the interplay between hard analysis and high-precision calculations.
Walsh Equiconvergence Of Complex Interpolating Polynomials
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Author : Amnon Jakimovski
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-16
Walsh Equiconvergence Of Complex Interpolating Polynomials written by Amnon Jakimovski 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 2007-05-16 with Mathematics categories.
This book is a collection of the various old and new results, centered around the following simple and beautiful observation of J.L. Walsh - If a function is analytic in a finite disc, and not in a larger disc, then the difference between the Lagrange interpolant of the function, at the roots of unity, and the partial sums of the Taylor series, about the origin, tends to zero in a larger disc than the radius of convergence of the Taylor series, while each of these operators converges only in the original disc. This book will be particularly useful for researchers in approximation and interpolation theory.
Recent Advances In Polynomials
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Author : Kamal Shah
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-05-18
Recent Advances In Polynomials written by Kamal Shah and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-18 with Mathematics categories.
This book provides a broad overview of recent developments in polynomials and their applications. It includes eight chapters that address such topics as characteristic functions of polynomials, permutations, Gon?arov polynomials, irreducible factors, polynomial regression algorithms, and the use of polynomials in fractional calculus, and much more.
Approximation Theory And Approximation Practice Extended Edition
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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2019-01-01
Approximation Theory And Approximation Practice Extended Edition written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-01 with Mathematics categories.
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.
Numerical Methods Based On Sinc And Analytic Functions
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Author : Frank Stenger
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Methods Based On Sinc And Analytic Functions written by Frank Stenger 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.
Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.
Polynomials
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Author : E.J. Barbeau
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-09
Polynomials written by E.J. Barbeau 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 2003-10-09 with Mathematics categories.
The book extends the high school curriculum and provides a backdrop for later study in calculus, modern algebra, numerical analysis, and complex variable theory. Exercises introduce many techniques and topics in the theory of equations, such as evolution and factorization of polynomials, solution of equations, interpolation, approximation, and congruences. The theory is not treated formally, but rather illustrated through examples. Over 300 problems drawn from journals, contests, and examinations test understanding, ingenuity, and skill. Each chapter ends with a list of hints; there are answers to many of the exercises and solutions to all of the problems. In addition, 69 "explorations" invite the reader to investigate research problems and related topics.
Mathematical Constants
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Author : Steven R. Finch
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-18
Mathematical Constants written by Steven R. Finch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-18 with Mathematics categories.
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.