Numerical AnalysisSee photo Given that the interpolation error isE,(x-x1)(x – x2) • ... (x – xµ).(n+ 1)!Why is the error reduced when the nodes x;'s are replaced with the roots of the Chebyshevpolynomial?

We have the interpolation error is En=fn+1ξ(n+1)!x-x1x-x2...x-xn Now, the roots of the Chebyshev…

Answered: Given that the interpolation error is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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hand written plzz The table shows the number of cars manufactured in thousands by a company for selected years. Use a calculator to write a quartic model for the number of cars manufactured in a given year since 2000. Then use the model to estimate the number of cars manufactured in 2011. 2005 2007 2008 2010 2012 Year Cars manufactured 138.5 183.1 194.8 204.3 242.8 (thousands) f(x) = 0.808x³+21.028x²-187.403x + 373.988 The estimated number of cars manufactured in 2011 is about 218. f(x) = 0.135x4-3.807x³ + 36.285x2-118.073x + 213.2 The estimated number of cars manufactured in 2011 is about 215. f(x) = 0.135x4 +3.807x³-36.285x2 + 118.073x - 213.2 The estimated number of cars manufactured in 2011 is about 215. f(x)=0.808x³ - 21.028x² + 187.403x373.988 The estimated number of cars manufactured in 2011 is about 218.
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Given that the interpolation error is E, (x – x1)(x – x2) ...· (x – xn). (n+1)! Why is the error reduced when the nodes x;'s are replaced with the roots of the Chebyshev polynomial?