A popular method for curve fitting is the “Least Squared&rdqu...

  1. Home
  2. Homework Library
  3. Mathematics
  4. Calculus
  5. A popular method for curve fitting is the “Least Squared&rdqu...

QuestionQuestion

Transcribed TextTranscribed Text

A popular method for curve fitting is the β€œLeast Squared” method. a) Determine the value of the constant k which best approximates a specified function f(x) on the interval π‘Ž ≀ π‘₯ ≀ 𝑏. Use as a cost function to be minimized: 𝐿(π‘˜) = 1 2 ∫ [π‘˜ βˆ’ 𝑓(π‘₯)] 2𝑑π‘₯ 𝑏 π‘Ž Verify that a minimum is achieved by checking the 2nd order optimality condition. b) Determine the optimal value of π‘˜ and 𝐿(π‘˜) in fractional form for 𝑓(π‘₯) = π‘₯ 2 , π‘Ž = 0, π‘Žπ‘›π‘‘ 𝑏 = 1. c) For the best linear fit, determine the optimal value of π‘˜, π‘š π‘Žπ‘›π‘‘ 𝐿(π‘˜) in fractional form for 𝑓(π‘₯) = π‘₯ 2 , π‘Ž = 0, π‘Žπ‘›π‘‘ 𝑏 = 1 where, 𝐿(π‘˜, π‘š) = 1 2 ∫ [π‘šπ‘₯ + π‘˜ βˆ’ 𝑓(π‘₯)] 2𝑑π‘₯ 𝑏 π‘Ž Hint: The answers to these problems can be confirmed using MATLAB’s or Excel’s curve fitting. In part a. we need to solve 𝑑𝐿(π‘˜) π‘‘π‘˜ = 0

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:
    Solution.pdf.

    50% discount

    Hours
    Minutes
    Seconds
    $25.00 $12.50
    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 Calculus 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.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    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