Interpolation and Approximation by Polynomials

1. Front Matter

   Pages i-xiv

   PDF

2. Univariate Interpolation

   • George M. Phillips

   Pages 1-48

3. Best Approximation

   • George M. Phillips

   Pages 49-118

4. Numerical Integration

   • George M. Phillips

   Pages 119-146

5. Peano’s Theorem and Applications

   • George M. Phillips

   Pages 147-162

6. Multivariate Interpolation

   • George M. Phillips

   Pages 163-214

7. Splines

   • George M. Phillips

   Pages 215-246

8. Bernstein Polynomials

   • George M. Phillips

   Pages 247-290

9. Properties of the q-Integers

   • George M. Phillips

   Pages 291-304

10. Back Matter

    Pages 305-312

    PDF

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.

• Approximation
• Interpolation
• Numerical integration
• approximation theory
• calculus

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)

• Mathematical Institute University of St. Andrews, St. Andrews, Scotland

  George M. Phillips

 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.

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