In this chapter, we deal with the problem of approximation of functions. A prototype problem can be described as follows: For some function f, known exactly or approximately, find an approximation that has a more simply computable form, with the error of the approximation within a given error tolerance. Often the function f is not known exactly. For example, if the function comes from a physical experiment, we usually have a table of function values only. Even when a closed-form expression is available, it may happen that the expression is not easily computable, for example,
KeywordsOrthogonal Polynomial Product Space Approximation Theory Chebyshev Polynomial Trigonometric Polynomial
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