Polynomials Of Best Approximation On A Real Finite Point Set
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Author | : Theodore Samuel Motzkin |
Publisher | : |
Total Pages | : 60 |
Release | : 1957 |
Genre | : Algebra |
ISBN | : |
A statement, without proof, is made for polynomials of best approximation to a given function on a real finite point set, E. These are important in numerical computation where they have various properties in common, especially those relating to oscillation of the difference on E.
Author | : Theodore Samuel Motzkin |
Publisher | : |
Total Pages | : 28 |
Release | : 1957 |
Genre | : Algebra |
ISBN | : |
A statement, without proof, is made for polynomials of best approximation to a given function on a real finite point set, E. These are important in numerical computation where they have various properties in common, especially those relating to oscillation of the difference on E.
Author | : J. L. Walsh |
Publisher | : |
Total Pages | : 24 |
Release | : 1959 |
Genre | : Polynomials |
ISBN | : |
Author | : Theodore J. Rivlin |
Publisher | : Courier Corporation |
Total Pages | : 164 |
Release | : 1981-01-01 |
Genre | : Mathematics |
ISBN | : 9780486640693 |
Mathematics of Computing -- Numerical Analysis.
Author | : Anton C. T. (Anton Ching-Tung) Chin |
Publisher | : |
Total Pages | : 156 |
Release | : 1984 |
Genre | : Approximation theory |
ISBN | : |
Author | : Frederick James Schuurmann |
Publisher | : |
Total Pages | : 212 |
Release | : 1967 |
Genre | : Functions |
ISBN | : |
Author | : Le Baron O. Ferguson |
Publisher | : American Mathematical Soc. |
Total Pages | : 174 |
Release | : 1980 |
Genre | : Mathematics |
ISBN | : 0821815172 |
Addresses two questions that include: 'What functions can be approximated by polynomials whose coefficients are integers?' and 'How well are they approximated (Jackson type theorems)?'
Author | : Ben Adcock |
Publisher | : SIAM |
Total Pages | : 310 |
Release | : 2022-02-16 |
Genre | : Mathematics |
ISBN | : 161197688X |
Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
Author | : Theodore Samuel Motzkin |
Publisher | : |
Total Pages | : 68 |
Release | : 1956 |
Genre | : Functions of complex variables |
ISBN | : |
Author | : Walter Edwin Sewell |
Publisher | : Princeton University Press |
Total Pages | : 251 |
Release | : 1943-01-20 |
Genre | : Mathematics |
ISBN | : 0691095728 |
A classic treatment of degree of approximation by polynomials in the complex domain from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.