QuestionQuestion

Transcribed TextTranscribed Text

1. Compute on paper the QR factorization of the following matrix using both classical and modified Gram-Schmidt algorithms. -8 3 2 -8 2 7 A= 3 2 - 1 2 7 - 1 4 2. Consider the system Ax = b where A is the matrix from problem 1) and b = [1 1 1 1]t. Solve the system using the QR factorization obtained in 1). 3. Consider the function f: Rm Rn defined by f fxx = Ax. Show that the Jacobian J is equal to A. (Hint: Start with a 2 X 3 matrix and generalize.) 4. Consider the regularized least squares problem min Il A.c - Show that the regularized problem is equivalent to the least squares problem 2 min x A b 2 Show that the normal equation of this new least squares problem is = Consider L = I, the identity matrix. Using the SVD of A, show that the solution of the normal equation is given by = 5. Show that computing 2.c by x + x is backward stable.

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.

    $50.00
    for this solution

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

    Find A Tutor

    View available Numerical Analysis 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