Abstract
In this chapter we present error estimates for the approximation of functions by orthogonal polynomials. The results will cover the following topics:
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(i)
inverse inequalities for polynomials concerning summability and differentiability;
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(ii)
error estimates for the truncation error u — P N u,where P N u denotes the truncated “Fourier” series of u;
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(iii)
existence, uniqueness and error estimates for the polynomials of best approximation in L Por Sobolev norms;
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(iv)
error estimates for the interpolation error u — I N u,where I N u denotes the polynomial interpolating u at a selected set of points in the domain.
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© 1988 Springer-Verlag Berlin Heidelberg
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Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A. (1988). Global Approximation Results. In: Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84108-8_9
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DOI: https://doi.org/10.1007/978-3-642-84108-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52205-8
Online ISBN: 978-3-642-84108-8
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