3. (10 pts) Sometimes we want to fit a given curve as closely as po...

  1. Home
  2. Homework Library
  3. Physics
  4. Physics - Other
  5. 3. (10 pts) Sometimes we want to fit a given curve as closely as po...


Transcribed TextTranscribed Text

3. (10 pts) Sometimes we want to fit a given curve as closely as possible by a polynomial of a given degree. The criterion of "Least Squares" is often used to determine the best fit. For example, if we want to fit a function f(x) on the interval (-1, - 1] by a polynomial of degree n, Er-o Ckrk we require the coefficients Ck to minimize the integral 1 n 2 1 Then fn (x) = ET-O Chrck is called the best approximation of f(x) (at order n.) in the least squares sense. Show that if we expand f(x) in Legendre series 2 1 f(x)= [auPe(x) where ae = 1 1 f(x) Pe(x) dx, e=0 the truncation of the sum up to l=n, n CaePe(x) e=0 gives the best polynomial (of degree n) approximation of f(x) in the interval [-1, 1].

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:

    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Physics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats