Winter 2006 UCLA EE 103 Homework Assignments

Formatting Instructions

• Put your solutions in the same order the problems are assigned in.
• On the front page of your HW submission, list the assignment number (e.g., HW 1), your full name, e-mail address, discussion section, and TA's name.
• On every page, please put your last name and the page number.
• You may hand-write your solutions or type them and submit a printout, including Matlab code and output. However, please edit any Matlab transcript so that it contains only the minimal amount of text and data necessary --- please don't waste paper. You may also prepare a well-ordered combination of handwritten and typed solutions.
• You may prepare typed homework in plain text, MS Word, or any other widely recognized format. Just organize it neatly so that the reader can follow it without difficulty.

Assignments

• Course Project due 4:00 PM, Thurs., 3/16 in lecture
  • Answers to Part 1 by Tae Roh.
  • Answers to Parts 2 and 3 by Seung Yang (except #12 and #14 below).
  • Answer to #12 (quadrature) by Tae Roh.
  • Answers to #14 (the linear program) by Tae Roh.

  Project Notes

  • 3/6/06 FAQ file posted Monday 3/6.

  • 3/2/06 A Matlab Encoding of the test function for the course project has been posted, including the encoding of its derivatives.
  • 3/3/06 A sample Matlab Implementation of minimization by steepest descent has been posted along with a detailed numerical example of its application. You may modify this code to implement the methods assigned in other exercises. A small numerical example of minimization by pure Newton steps has also been posted.
  • 3/3/06 In Exercise 7, please ignore the nonsensical request to "Compare both versions of the linesearch described in the preceding exercise..."

• HW 6 due 4:00 PM, Thurs., 2/23, in lecture
  Solutions by Seung Yang
• HW 5 due 4:00 PM, Thurs., 2/16, in lecture; Solutions [.pdf] by Tae Roh.
  3.9 (a) (simply estimate the domain of convergence empirically, using rungeinterp.m), 5.4 (you may restrict to real matrices), 5.5, 5.7, 5.8, 5.11 (a) (b); see http://www.itl.nist.gov/div898/strd/lls/data/Longley.shtml.

• HW 4 due 4:00 PM, Thurs., 2/9, in lecture (extended 2 days) Solutions by Seung Yang
• Linear Algebra Review
• Partial Solutions and Hints [.pdf]
• Partial Solution for Exercise 6 [.pdf] (Updated 7:40pm Mon. 2/6)
  For the more challenging parts of Exercise 6, careful consideration of particular examples of rref similar to the one given will be accepted in lieu of formal proof.
• HW 3 due 4:00 PM, Thurs., 2/2, in lecture (extended 2 days) Solutions [.pdf] by Tae Roh.
  • Moler Ch. 2 pp. 82 ff. Exercises 5 (implement Cholesky factorization in Matlab), 14, 17a, 19
  • Given the n by n matrix A and the n by 1 vector b, which is the more efficient way to solve the linear system A³x = b for x?
    1. Compute A³ = A * A * A, find its LU factorization, PA³ = LU, then solve LUx = Pb.
    2. Compute the LU factorization of A, PA = LU, then use it to solve the systems PAz = Pb for z, PAy = Pz for y, and PAx = Py for x in sequence.
    Prove your answer.

• HW 2 due 4:00 PM, Tues., 1/24, in lecture
  Solutions by Seung Yang; Last problem by Prof. Shinnerl.
  • Moler Ch. 2 pp. 82 ff. Exercises 3, 4, 10, 11
  • Additional exercises posted here For supplemental problem 4 (harmonic series "convergence" in floating point), please use the chop function to perform all sums in 4-decimal-digit arithmetic.

• HW 1 due 4:00 PM, Thurs., 1/19, in lecture Solutions by Tae Roh.
  • Redo the pre-test carefully.
  • Moler Ch. 1 pp. 41 ff. Exercises 1, 4, 6, 7, 8, 17, 19, 32, 35, 37, 38, 39, 45