Solution Found!
Find the trigonometric polynomial F(x) of the form (2) for which the square error with respect to the given f(x) on the interval \(-\pi<x<\pi\) is minimum. Compute the minimum value for \(N=1,2, \cdots, 5\) (or also for larger values if you have a CAS). \(f(x)=
Chapter 11, Problem 3(choose chapter or problem)
QUESTION:
Find the trigonometric polynomial F(x) of the form (2) for which the square error with respect to the given f(x) on the interval \(-\pi<x<\pi\) is minimum. Compute the minimum value for \(N=1,2, \cdots, 5\) (or also for larger values if you have a CAS).
\(f(x)=|x| \quad(-\pi<x<\pi)\)
Questions & Answers
QUESTION:
Find the trigonometric polynomial F(x) of the form (2) for which the square error with respect to the given f(x) on the interval \(-\pi<x<\pi\) is minimum. Compute the minimum value for \(N=1,2, \cdots, 5\) (or also for larger values if you have a CAS).
\(f(x)=|x| \quad(-\pi<x<\pi)\)
ANSWER:Step 1 of 4
The statement is given as the Prob. 5's square mistakes are significantly bigger than Prob. 3's.