Fundamentals of Approximation Theory
Alpha Science International, 2007 - Mathematics - 545 pages
"This book presents a systematic and in-depth treatment of some basic topics in approximation theory in an effort to emphasize the rich connections of different branches of analysis with this subject. It contains a good blend of both the classical as well as abstract topics in the domain and their interconnections as appropriate. The approach is from the very concrete to more and more abstract levels. In order to provide a historical perspective on the results, a section on notes is appended to each chapter with an extensive bibliography. Researchers will find several references to recent developments. Problems of varying degree of difficulty accompany each chapter. Some of these problems complement certain results from the text. The others, more challenging, are drawn from the contemporary research articles. Ample hints are provided for such problems." "Primarily aimed at graduate students and teachers of mathematics, researchers interested in an introduction to the specific results or techniques of approximation theory will find this book very attractive."--BOOK JACKET.
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Linear Chebyshev Approximation
Degree of Approximation
7 other sections not shown
AK(X algorithm assume B-splines Banach space bounded called Cent Chebyshev polynomials CLB(X CLC(X closed coefficients compact subset completes the proof conclude constant continuous function continuous selection contradicts convergent convex set convex subset Corollary crit data nodes defined Definition denote dense distinct points distinct zeros dv(x equations exists Ext U(X finite dimensional following theorem Fourier series given Haar condition Haar subspace Hausdorff Hausdorff space Hence Hermite interpolation implies inequality integer interval Lemma Let f linear subspace lower semicontinuity matrix metric projection multifunction nonempty normed linear space normed space observe obtain optimal orthogonal polynomials poised proof of Theorem Proposition prove proximinal Pv(x Py(x rad v(F reader resp result rotund satisfying Section sequence smooth spline interpolant statements are equivalent Suppose topological trigonometric polynomials uniformly unique best approximation unique element unique solution