Function interpolation may be carried out using algebraic polynomial, splines, Fourier polynomial, rational functions, wavelets, or Sinc methods. In this chapter we describe methods for getting a more uniform approximation throughout the interval of approximation in the cases when the magnitude of the errors of interpolation is either much larger at one endpoint of the interval than the other, or when the magnitudes of the errors at endpoints are roughly the same, but differ considerably from those errors in the mid-range of the interval. We also discuss improving approximation of the derivative obtained by differentiating the constructed interpolation approximations. This chapter extends the recently obtained results of (Stenger, J Complex 25:292–302, 2009).
Distinct Point Polynomial Approximation Polynomial Interpolation Sinc Method Arbitrary Positive Number
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