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.
|This book is intended as a course in numerical analysis and approximation theory for advanced undergraduate students or graduate students, and as a reference work for those who lecture or research in this area. Its title pays homage to Interpolation and Approximation by Philip J. Davis, published in 1963 by Blaisdell and reprinted by Dover in 1976. My book is less g- eral than Philip Davis´s much respected classic, as the quali?cation "by polynomials” in its title suggests, and it is pitched at a less advanced level. I believe that no one book can fully cover all the material that could appearinabookentitledInterpolation and Approximation by Polynomials. Nevertheless, I have tried to cover most of the main topics. I hope that my readers will share my enthusiasm for this exciting and fascinating area of mathematics, and that, by working through this book, some will be encouraged to read more widely and pursue research in the subject. Since my book is concerned with polynomials, it is written in the language of classical analysis and the only prerequisites are introductory courses in analysis and linear algebra.|This book is aimed at advanced undergraduate students and graduate students and is intended for a course in numerical analysis and approximation theory. The author covers topics such as multivariate interpolation, Peano kernel theory, and the applications of q-integers to approximation theory, the latter of which have never been fully examined in book form before.
* Preface * Univariate Interpolation * Best Approximation * Numerical Integration * Peano's Theorem and Applications * Multivariate Interpolation * Splines * Bernstein Polynomials * Properties of the q-integers * References * Index *
This book covers the main topics concerned with interpolation and approximation by polynomials. This subject can be traced back to the precalculus era but has enjoyed most of its growth and development since the end of the nineteenth century and is still a lively and flourishing part of mathematics. 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.
George Phillips has lectured and researched in mathematics at the University of St. Andrews, Scotland. His most recent book, Two Millenia of Mathematics: From Archimedes to Gauss (Springer 2000), received enthusiastic reviews in the USA, Britain and Canada. He is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
From the reviews:
G.M. Phillips
Interpolation and Approximation by Polynomials
"A very nicely written textbook to learn about polynomial interpolation and approximation."
—ZENTRALBLATT MATH
"This book contains selected topics from approximation theory. The author discusses one of `the most´ classic part of approximation theory, the interpolation theory and two related fields ... . The selection of the areas, the lot of worked examples, the exercises and problems at the end of each section and the algorithms included and detailed ... makes this book perfect for everyone´s approximation book." (Béla Nagy, Acta Scientiarum Mathematicarum, Vol. 69, 2003)
"This is a very nicely written textbook to learn about polynomial interpolation and approximation. ... Throughout the book nice sets of `Problems´ are placed ... ." (Marcel G. de Bruin, Zentralblatt MATH, Vol. 1023, 2003)
"This monograph may be considered as the successor of P. Davis´ Interpolation and Approximation (1963) ... . it is an excellent introduction to the topic. ... This book is well suited for a course on numerical analysis and approximation theory with emphasis on the topic mentioned in the title. ... even more a course book because each section ends with a list of exercises, and the text contains many explicit examples.” (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, 2007)
This book is intended as a course in numerical analysis and approximation theory for advanced undergraduate students or graduate students, and as a reference work for those who lecture or research in this area. Its title pays homage to Interpolation and Approximation by Philip J. Davis, published in 1963 by Blaisdell and reprinted by Dover in 1976. My book is less g- eral than Philip Davis's much respected classic, as the quali?cation "by polynomials" in its title suggests, and it is pitched at a less advanced level. I believe that no one book can fully cover all the material that could appearinabookentitledInterpolation and Approximation by Polynomials. Nevertheless, I have tried to cover most of the main topics. I hope that my readers will share my enthusiasm for this exciting and fascinating area of mathematics, and that, by working through this book, some will be encouraged to read more widely and pursue research in the subject. Since my book is concerned with polynomials, it is written in the language of classical analysis and the only prerequisites are introductory courses in analysis and linear algebra.
Univariate Interpolation.- Best Approximation.- Numerical Integration.- Peano's Theorem and Applications.- Multivariate Interpolation.- Splines.- Bernstein Polynomials.- Properties of the q-Integers.
From the reviews:
G.M. Phillips
Interpolation and Approximation by Polynomials
"A very nicely written textbook to learn about polynomial interpolation and approximation."
-ZENTRALBLATT MATH
"This book contains selected topics from approximation theory. The author discusses one of 'the most' classic part of approximation theory, the interpolation theory and two related fields ... . The selection of the areas, the lot of worked examples, the exercises and problems at the end of each section and the algorithms included and detailed ... makes this book perfect for everyone's approximation book." (Béla Nagy, Acta Scientiarum Mathematicarum, Vol. 69, 2003)
"This is a very nicely written textbook to learn about polynomial interpolation and approximation. ... Throughout the book nice sets of 'Problems' are placed ... ." (Marcel G. de Bruin, Zentralblatt MATH, Vol. 1023, 2003)
"This monograph may be considered as the successor of P. Davis' Interpolation and Approximation (1963) ... . it is an excellent introduction to the topic. ... This book is well suited for a course on numerical analysis and approximation theory with emphasis on the topic mentioned in the title. ... even more a course book because each section ends with a list of exercises, and the text contains many explicit examples." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, 2007)
George Phillips has lectured and researched in mathematics at the University of St. Andrews, Scotland. His most recent book, Two Millenia of Mathematics: From Archimedes to Gauss (Springer 2000), received enthusiastic reviews in the USA, Britain and Canada. He is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Über den Autor
George Phillips has lectured and researched in mathematics at the University of St. Andrews, Scotland. His most recent book, Two Millenia of Mathematics: From Archimedes to Gauss (Springer 2000), received enthusiastic reviews in the USA, Britain and Canada. He is well known for his clarity of writing and his many contributions as a researcher in approximation theory.
Inhaltsverzeichnis
* Preface * Univariate Interpolation * Best Approximation * Numerical Integration * Peano's Theorem and Applications * Multivariate Interpolation * Splines * Bernstein Polynomials * Properties of the q-integers * References * Index *
This book is aimed at advanced undergraduate students and graduate
students and is intended for a course in numerical analysis and
approximation theory. The author covers topics such as multivariate
interpolation, Peano kernel theory, and the applications of q-integers
to approximation theory, the latter of which have never been fully
examined in book form before.
