Approximation Theory and Approximation PracticeThis book presents a twenty-first century approach to classical polynomial and rational approximation theory. The reader will find a strikingly original treatment of the subject, completely unlike any of the existing literature on approximation theory, with a rich set of both computational and theoretical exercises for the classroom. There are many original features that set this book apart: the emphasis is on topics close to numerical algorithms; every idea is illustrated with Chebfun examples; each chapter has an accompanying Matlab file for the reader to download; the text focuses on theorems and methods for analytic functions; original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. This textbook is ideal for advanced undergraduates and graduate students across all of applied mathematics. |
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Approximation Theory and Approximation Practice, Extended Edition Lloyd N. Trefethen Limited preview - 2019 |
Common terms and phrases
accuracy algorithm analytic appear applications barycentric Bernstein best approximation bounded called Chapter Chebfun Chebyshev interpolants Chebyshev points Chebyshev polynomials Chebyshev series circle ClenshawICurtis close coefficients command complex compute condition consider construct continuous contour convergence corresponding curve defined derivative difference differential discussion effect eigenvalues ellipse equal equations equioscillation equispaced error evaluate exact example Exercise exponential fact find first formula function f Gauss quadrature geometric given gives grid hold idea implies integral interval known Lagrange Lebesgue constants Legendre linear look Math mathematics Matlab matrix methods Note null vector numerical operator Padé approximation particular plane plot poles polynomial interpolants practical precision problem projection proof proved quadrature rational approximation rational functions result roots Show singularities solution square Suppose Taylor Theorem transformed Trefethen unique unit values vector weights zero