Let så be the least squares approximation (best approximation in the L² norm, || · ||2)of a 27 periodic, continuous function f by a trigonometric polynomial of degree atmost n and let pn be the interpolating trigonometric of ƒ at 2n – 1 points.-(a) Prove that||f - Sn||2 ≤ f - Pn||2.(1)

Answered: Image /qna-images/answer/18bc6589-c433-42e7-9165-793fd3280eaa.jpg

Answered: Let Sn be the least squares…

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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Let Sn be the least squares approximation (best approximation in the L² norm, || of a 2 periodic, continuous function f by a trigonometric polynomial of degree most n and let på be the interpolating trigonometric of ƒ at 2n – 1 points. (a) Prove that ||f8n||2 ≤ f - Pn||2.