1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Interpolating polynomial for sin([itex]\pi{x}[/itex])

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data
    Consider the function sin([itex]\pi[/itex][itex]x[/itex]) on [-1,1] and its approximations by interpolating polynomials. For integer [itex]n[/itex][itex]\geq[/itex]1, let [itex]x_{n,j}=-1+\frac{2j}{n}[/itex] for [itex]j=0,1,...,n[/itex], and let [itex]p_{n}(x)[/itex] be the [itex]n[/itex]th-degree polynomial interpolating sin([itex]\pi[/itex][itex]x[/itex]) at the nodes [itex]x_{n,0},...,x_{n,n}[/itex]. Prove that

    [itex]\max_{x\in[-1,1]}\left | {sin}{(\pi{x})-p_{n}{(x)}} \right | \to 0[/itex] as [itex]n \to \infty[/itex]


    2. Relevant equations



    3. The attempt at a solution
    I have no idea how to start!!!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Interpolating polynomial for sin([itex]\pi{x}[/itex])
  1. Matlab dy/dx=sin(x) (Replies: 0)

Loading...