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!

Polynomial interpolation

  1. Apr 10, 2010 #1
    Let [tex]x_{0}, x_{1}, \cdots , x_{n}[/tex] be distinct points in the interval [a,b] and [tex]f \in C^{1}[a,b][/tex].

    We show that for any given [tex]\epsilon >0[/tex] there exists a polynomial p such that

    [tex]\left\| f-p \right\|_{\infty} < \epsilon[/tex] and [tex]p(x_{i}) = f(x_{i})[/tex] for all [tex]i=1,2, \cdots , n [/tex]

    I know [tex]\left\| f\right\| _{\infty}= max_{x \in [a,b]}|f(x)| [/tex] and I wonder if the polynomial they are asking for is the Lagrangian polynomial interpolating f at the nodes [tex]x_{0}, x_{1}, \cdots , x_{n}[/tex]. If yes, I am not sure how to prove the problem.
     
  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?
Draft saved Draft deleted