Abstract
In the present chapter we give some basic tools to define and analyze trigonometric approximation methods. We first discuss the one dimensional case and study the approximation properties of the orthogonal projection and the interpolation projection. In addition to the standard polynomial approximation we derive also estimates of an exponential type. Moreover, we consider two dimensional interpolation and derive error estimates in a framework of the Sobolev spaces H μ1,μ2 and H μ1 (ℝ2) of biperiodic functions.
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© 2002 Springer-Verlag Berlin Heidelberg
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Saranen, J., Vainikko, G. (2002). Trigonometric Interpolation. In: Periodic Integral and Pseudodifferential Equations with Numerical Approximation. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04796-5_8
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DOI: https://doi.org/10.1007/978-3-662-04796-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07538-4
Online ISBN: 978-3-662-04796-5
eBook Packages: Springer Book Archive