Approximations and Expansions
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|Dave Rusin; The Mathematical Atlas|
|A short article designed to provide an introduction to approximations and expansions, which primarily concern the approximation of classes of real functions by functions of special types. This includes approximations by linear functions, polynomials (not just the Taylor polynomials), rational functions, and so on; approximations by trigonometric polynomials is separated into Fourier analysis (below). Topics include criteria for goodness of fit, error bounds, stability upon change of approximating family, and preservation of functional characteristics (e.g. differentiability) under approximation. Effective techniques for specific kinds of approximation are also prized. This is also the area covering interpolation and splines. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.|
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