Theory of Approximation (Dover Phoenix Editions)

Rating:
Summary: The fundamentals.
Review: Even at a time when a subject undergoes a revolution, and new directions keep coming, new methods; even brand new and different applications--- even then are there central ideas that are constant, the fundamentals. Within mathematics, approximation theory is such a field: In the past decade, we have seen a host of such new developments: wavelet approximations, fast computational algorithms with applications to turbulence, chaos and fractals; computational efficiencies from scaling similarities, and data compression; and new adaptive non-linear algorithms. The author Achieser of this Dover classic (first published by Ungar in 1956, and reprinted by Dover in 1992) is a pioneer in the approximation theory, and the book is still a very attractive first. I recommend it to students even today! Achieser's lovely book begins with the fundamentals on normed spaces, and it has the classical theorems of Weierstrass, Muntz, and Riesz. The other topics range from the incisive ideas of Tchebysheff and Haar to harmonic approximation. From extremal properties of transcendental functions to Wiener's general Tauber theorem, and more.
Review by Palle Jorgensen, October 2003.

Rating:
Summary: an encyclopedia of results in approximation theory
Review: This should be on the reading list of every graduate student in control or signal processing. This book is an encyclopedia of results in approximation theory including Chebyshev approximation, harmonic analysis, and extremal properties of integral transcendental functions. The exposition is terse in some places and the proofs are sometimes sketchy, but the examples are really great. The focus on the ideas is excellent.

Rating:
Summary: an encyclopedia of results in approximation theory
Review: This should be on the reading list of every graduate student in control or signal processing. This book is an encyclopedia of results in approximation theory including Chebyshev approximation, harmonic analysis, and extremal properties of integral transcendental functions. The exposition is terse in some places and the proofs are sometimes sketchy, but the examples are really great. The focus on the ideas is excellent.