Course Announcements

12/17/24

1. Anonymous semester points and grade distribution for Fall 2024 posted.

2. Letter grade distribution for Fall 2022, 2023 and 2024 posted for comparison and your reference.

3. Anonymous Final Exam grade distribution for Fall 2024 posted.

4. Your Final Exam can be examined by appointment between the semesters. The exam must be retained by the instructor according to university policy.

12/10/24

1. Comments on Program 4 and Matlab codes for all methods and testing have been posted.

12/8/24

1. Comments on Program 3 and Matlab codes for all methods and testing have been posted.

12/4/24

1. Some extra information on Broyden's method for nonlinear systems has been added to the summary on slides 52 and 53.

11/30/24

1. Program 4 has been posted.

2. I will be available next week at most times for appointments to answer review questions in preparation for the Final Exam. Currently, the only times I am definitely not available are 8:30 to 10:00 on Wednesday due to a PhD student's examination and MWF 13:20 to 14:45 due to a class.

11/29/24

1. Solutions to the Written Problems of Homework 3 have been posted.

2. The final programming assignment will be posted tomorrow morning. It will not require extensive experimentation like earlier assignments, rather you may respond using a few tests described appropriately, e.g., with some tables or a curve. These will be in response to specific questions based on the notes and some problems in Study Question Set 6. You will need an implementation of Regular Falsi, Secant and Newton methods. Additionally, you will compare them to a quadratically convergent method call Steffensen's method that will be described in the assignment.

3. Since this assignment is less involved it will be worth less than the 100 points of the earlier homeworks. It will be due the Monday of Final Exam week, i.e., you will have 9 days to complete it.

11/25/24

1. Sets 14 and 15 of the class notes have been posted.

2. Solutions for Study Question Set 6 have been posted.

11/22/24

1. Study Questions Set 6 has been posted.

11/21/24

1. Set 13 of the class notes has been posted. You are not responsible for the proofs only the results for Regular Falsi, Secant and Newton methods. These will be discussed in class. You are however encouraged to read the proofs at some point since the technique is commonly used to analyze local model-based iterations in areas such as optimization.

11/19/24

1. Set 12 of the class notes has been posted. It is imperative that you read ahead in Set 11 and 12 to prepare for this week's lectures.

11/18/24

1. The typo of Tx=f has been corrected to Ax=b in Problem 3.2 of the written homework problems.

11/15/24

1. Set 11 of the class notes has been posted.

11/12/24

1. The written problems for Homework 3 have been posted.

2. Programming Assignment 3 has been posted.

11/8/24

1. Study Questions Set 5 and the solutions have been posted.

2. Matlab codes for the Householder reflector based code for linear least squares generation and solution have been posted.

11/6/24

1. Set 10 of the class notes has been posted.

11/5/24

1. Set 9 of the class notes has been posted.

2. Slide 32 in Set 8 has been modified to clarify the motivation for the projection.

3. A new slide 33 has been added to Set 8 that sets out the relationship of the stepsize selection with a local optimization problem.

11/3/24

1. An anonymous curve of grades on the Midterm Exam has beenn posted under the Grades tab on the class departmental page. The exams will be available in class tomorrow.

2. The exam was designed to have a good score in the mid 50s.

3. It is strongly recommended you read the solutions carefully before discussing the exam with me or Yue. Such a discussion is strongly recommended for those scoring below 50.

10/31/24

1. Study Questions Set 4 has been posted along with the solutions. This contains questions that include proofs of the results in the basic theory slides of Set 7. It is very important to be familiar with these results and techniques in order to understand the material on Richardson's methods, Steepest Descent and CG.

10/28/24

1. Set 8 of the class notes has been posted.

10/23/24

1. Set 7 of the class notes has been posted.

10/23/24

1. Dense array data structure notes have been added to Set 6 and the typo identified on slide 21 during class has been fixed.

2. Solutions for the Midterm Exam have been posted.

10/17/24

1. The remaining Matlab routines for Program 2 have been posted.

2. Comments on the solution of Program 2 have been posted.

10/14/24

1. Set 6 of the class notes has been posted.

10/9/24

1. Slides 32, 33 and 34 in Set 4 have been modified to fix a typo. The tildes were missing on the updated B matrix, i.e., the n-1 x n-1 matrix that defines the 2,2 blocks in L and U. The associated elements of the matrix on 33 and 34 have also had tildes added.

2. A clarification has been added to Program 2 to give the definition of the absolute value of a matrix that is denoted | B |. This does not mean determinant. It is the matrix with elements that are the absolute values of the corresponding elements in the matrix B.

3. The tracking of the condition number of a matrix that is factored and the growth factor seen when applying a particular pivoting strategy should be used in concert with examining the corresponding factorization error and solution error. The source of these trends will be discussed in the numerical stability lectures. Your observations can be the basis for an hypothesis on your part of what the values might indicate to a library designer or user.

10/7/24

1. Study Questions Set 2 and the solutions have been posted.

2. A clarification of Empirical Task 1 for Program 2 has been added to the Homework page.

10/2/24

1. Program 2 has been posted.

2. The time and place of the Midterm Exam has been posted.

9/30/24

1. Set 5 has been posted. It covers linear least squares, a transformation-based standard algorithm, and using the form of the transformed coordinate system derives a fundamental property of optimization which leads to a fundamental theorem of vector spaces. It is imperative you read ahead in this set. It is the last topic to be covered on the midterm.

2. Information on the Midterm Exam has been posted.

9/28/24

1. Set 4 has been updated with a clarifying example and associated lemma on the structure of the permuted Gauss transformations.

9/23/24

1. Solutions for the written problems and comments on the design of the codes for Program 1 have been posted.

2. Codes for Program 1 have been posted. A simpler driver for testing the compressed storage and banded lower triangular matrix vector multiplication will be posted.

3. The solutions for Study Questions Set 2 have been posted.

9/20/24

1. Study Question Set 2 has been posted.

9/18/24

Codes for lower and upper triangular systems have been posted on the Homework page. These are for your reference and will be useful for the LU factorization programming assignment soon to be made.

A minor typo in Set 3 has been fixed.

Set 4 has been modified in the discussion of Gaussian elimination and the transformation-based view. We discussed part of this on Monday and these modifications clarify significantly some of the slides. We will go over it again on Wednesday, i.e., today.

9/12/24

1. Some clarifying material and new code has been added to Set 3. Some minor typos have been fixed.

2. Set 4 of the class notes has been posted. It is strongly recommended that you read ahead in this set in preparation for the associated lectures.

9/6/24

1. Written Problems and Program Set 1 have been posted.

9/3/24

1. Solutions for Study Question Set 1 have been posted.

8/30/24

1. Some examples of matrix multiplication have been added to Set 2 and it has been reposted.

2. A list of some reference textbooks has been reposted.

8/28/24

1. Study Questions Set 1 has been posted.

8/26/24

1. The class syllabus has been posted.

2. Sets 1, 2 and 3 have been posted.

3. A description of the format for submitting program solutions has been posted.

4. Example program solutions have been posted.