Fundamentals of Approximation Theory
Alpha Science International, 2007 - Mathematics - 545 pages
The subject of approximation theory plays an increasingly important role in applications to many branches of applied sciences and engineering. Written in the span of almost a decade, Fundamentals of Approximation Theory serves as both an introductory text as well as an advanced review of the field. The first five chapters give the reader the core information to begin research in this domain. The next three chapters devote attention to special topics, exposing the reader to complex analytic methods and techniques of functional analysis. The authors emphasize the connections between different branches of analysis with approximation theory - between the 'classical' and the 'abstract.' They also include noteworthy features such as K-functionals, Hermite-Birkhoff interpolation, Lagrange-Hermite-Fejr-type interpolation, and complex methods in the treatment of Fourier series.
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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