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.
Interpolation and Approximation by Polynomials
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Book Description
Editorial Reviews
Review
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)
From the Back Cover
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.
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3 of 3 people found the following review helpful:
5.0 out of 5 stars
Great reference book, well written,
This review is from: Interpolation and Approximation by Polynomials (Hardcover)
I would recommend this book to anyone interested in numerical analysis, applied mathematics or approximation theory. First because polynomials are often the foundation and this books gives you much of the knowledge and basic tricks needed to be in control of them. Secondly because this book is a little gem of clarity that will enlighten you to the point where you may start to get a glimps of the beauty of mathematics. It is very well written book and joy to read.
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Inside This Book
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First Sentence:
Given the values of a function f(x) at two distinct values of x, say x0 and x1, we could approximate f by a linear function p that satisfies the conditions p(x0) = f(x0) and p(x1) = f(x1). (1.1) Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
trapezoidal rule with end correction, equioscillation points, weighted square norm, divided difference form, linear interpolating polynomial, truncated power function, forward difference form, minimax polynomial, minimax approximation, fundamental polynomial, leading coefficient unity, spaced abscissas, composite trapezoidal rule, polygonal arc, interpolating points, turning value, total positivity, difference formula, blending function, error terns, divided differences, empty product, recurrence relation, orthogonal series, midpoint rule Key Phrases - Capitalized Phrases (CAPs): (learn more)
Newton Cotes, Euler Maclaurin, Further Results, Graph of the B-spline, Neville Aitken New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Given the values of a function f(x) at two distinct values of x, say x0 and x1, we could approximate f by a linear function p that satisfies the conditions p(x0) = f(x0) and p(x1) = f(x1). (1.1) Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
trapezoidal rule with end correction, equioscillation points, weighted square norm, divided difference form, linear interpolating polynomial, truncated power function, forward difference form, minimax polynomial, minimax approximation, fundamental polynomial, leading coefficient unity, spaced abscissas, composite trapezoidal rule, polygonal arc, interpolating points, turning value, total positivity, difference formula, blending function, error terns, divided differences, empty product, recurrence relation, orthogonal series, midpoint rule Key Phrases - Capitalized Phrases (CAPs): (learn more)
Newton Cotes, Euler Maclaurin, Further Results, Graph of the B-spline, Neville Aitken New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 29
books:
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10
books
cite this book:
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- Theory and Applications of Numerical Analysis, Second Edition by G. M. Phillips in Front Matter, and Back Matter
- Approximation Theory (Proceedings of Symposia in Applied Mathematics) by Carl De Boor on page 113, and Back Matter
- Best Approximation in Inner Product Spaces by Frank R. Deutsch in Front Matter, and Back Matter
- Total Positivity, Volume One by Samuel Karlin in Back Matter
- Approximation Theory and Methods by M. J. D. Powell in Back Matter
See all 29 books this book cites
- Numerische Mathematik (Springer-Lehrbuch) (German Edition) by Robert Schaback in Back Matter
- Differential Geometry of Varieties with Degenerate Gauss Maps (CMS Books in Mathematics) by Maks A. Akivis in Front Matter
- Combinatorial Methods: Free Groups, Polynomials, and Free Algebras (CMS Books in Mathematics) by Vladimir Shpilrain in Front Matter
- Trends and Applications in Constructive Approximation (International Series of Numerical Mathematics) by Detlef H. Mache on page 51
- Techniques of Variational Analysis (CMS Books in Mathematics) by Jonathan M. Borwein in Front Matter
See all 10 books citing this book
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