Approximation of Functions in the Mean
| Author | : Academ Steklov Institute Of Math |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 310 |
| Release | : 1970-03 |
| Genre | : Mathematics |
| ISBN | : 9780821818886 |
Approximation Of Functions In The Mean
Download Approximation Of Functions In The Mean full books in PDF, epub, and Kindle. Read online free Approximation Of Functions In The Mean ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Theory of Approximation of Functions of a Real Variable
| Author | : A. F. Timan |
| Publisher | : Elsevier |
| Total Pages | : 644 |
| Release | : 2014-07-22 |
| Genre | : Mathematics |
| ISBN | : 1483184811 |
Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.
An approximation to the mean and variance of a certain function
| Author | : Mark Othello Glasgow |
| Publisher | : |
| Total Pages | : 38 |
| Release | : 1949 |
| Genre | : Functions |
| ISBN | : |
Approximation Theory and Approximation Practice, Extended Edition
| Author | : Lloyd N. Trefethen |
| Publisher | : SIAM |
| Total Pages | : 375 |
| Release | : 2019-01-01 |
| Genre | : Mathematics |
| ISBN | : 1611975948 |
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.
Approximation with Rational Functions
| Author | : Donald J. Newman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 58 |
| Release | : 1979-12-31 |
| Genre | : Mathematics |
| ISBN | : 0821816918 |
This series of lectures treats certain amusing and interesting aspects of rational function approximations, striving for variety and diversity rather than depth or thoroughness. Graduate students and faculty, knowledgeable in the elements of real and complex analysis, should gain insight into recent developments in the field.
Moduli of Smoothness
| Author | : Z. Ditzian |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 233 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461247780 |
The subject of this book is the introduction and application of a new measure for smoothness offunctions. Though we have both previously published some articles in this direction, the results given here are new. Much of the work was done in the summer of 1984 in Edmonton when we consolidated earlier ideas and worked out most of the details of the text. It took another year and a half to improve and polish many of the theorems. We express our gratitude to Paul Nevai and Richard Varga for their encouragement. We thank NSERC of Canada for its valuable support. We also thank Christine Fischer and Laura Heiland for their careful typing of our manuscript. z. Ditzian V. Totik CONTENTS Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 PART I. THE MODULUS OF SMOOTHNESS Chapter 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1. Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2. Discussion of Some Conditions on cp(x). . . . • . . . . . . . • . . • . . • • . 8 . . . • . 1.3. Examples of Various Step-Weight Functions cp(x) . . • . . • . . • . . • . . . 9 . . • Chapter 2. The K-Functional and the Modulus of Continuity ... . ... 10 2.1. The Equivalence Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . 10 . . . . . . . . . 2.2. The Upper Estimate, Kr.tp(f, tr)p ~ Mw;(f, t)p, Case I . . . . . . . . . . . . 12 . . . 2.3. The Upper Estimate of the K-Functional, The Other Cases. . . . . . . . . . 16 . 2.4. The Lower Estimate for the K-Functional. . . . . . . . . . . . . . . . . . . 20 . . . . . Chapter 3. K-Functionals and Moduli of Smoothness, Other Forms. 24 3.1. A Modified K-Functional . . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . 3.2. Forward and Backward Differences. . . . . . . . . . . . . . . . . . . . . . 26 . . . . . . . 3.3. Main-Part Modulus of Smoothness. . . . . . . . . . . . . . . . . . . . . . 28 . . . . . . .
Approximation of Functions
| Author | : G. G. Lorentz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 208 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 9780821840504 |
This is an easily accessible book on the approximation of functions--simple and without unnecessary details, but complete enough to include the main results of the theory. Except for a few sections, only functions of a real variable are treated. This work can be used as a textbook for graduate or advanced undergraduate courses or for self-study. Included in the volume are Notes at the end of each chapter, Problems, and a selected Bibliography.
Approximation of Functions and Operators
| Author | : S. B. Stechkin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 220 |
| Release | : 1977 |
| Genre | : Mathematics |
| ISBN | : 9780821830383 |
Papers and articles about approximation theory.
