7. Trigonometric interpolation

How can we understand the efficiency of Chebyshev interpolation between points? By noting that it's also trigonometric interpolation of even periodic functions between equidistant points! To see this, let's change the variable again

x = \cos ϕ \Leftrightarrow ϕ = \arccos x

^( 37 )

and use

T_{k} (x) = \cos (k

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Trigonometric interpolation

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page Application to derivation and integration

Linear barycentric rational interpolation

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Bibliography

(1) - BAKER (G.A.) Jr., GRAVES MORRIS (P.R.) - Padé Approximants, 2 ^nd ed - Cambridge University Press (1966).
(2) - BALTENSPERGER (R.) - Some results on linear rational trigonometric interpolation -...

Software

Chebfun Version 4.2 by TREFETHEN (L.N.) and the Chebfun Development Team 2011 :

http://www.maths.ox.ac.uk/chebfun/

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