Course Announcements

5/3/24: 1. An anonymous semester point and grade distribution has been posted.
4/28/24: 1. An anonymous grade distribution for Homework 7 has been posted.; 2. An anonymous semester points so far distribution for the Graded Homework Students has been posted. It will be updated when HW 3 is graded but clearly it is the 35 Final Exam semester points that it the large unknown in terms of letter grades. The letter grades will be assigned based on a curve of student performance and my expectations based on the design of the exams and homeworks for a particular accomplishment, e.g., above or below C-.
4/27/24: 1. Solutions for Homework 7 have been posted.
4/26/24: 1. Typos in the solutions of problem 5.3(a) and 6.3(b) have been fixed and the solutions reposted.
4/23/24: 1. The anonymous grade distribution have been posted for Homework 6 has been posted and the grades have been posted on Canvas.
4/23/24: 1. Anonymous grade distributions have been posted for Homeworks 4 and 5 and the grades have been posted on Canvas.; 2. The solutions for Homework 5 have been reloaded with a corrected solution for Problem 3.
4/20/24: 1. Solutions for Homework 6 have been posted.; 2. Information on the coverage of the Final Exam has been posted under the "Exams" button link.; 3. Householder QR factorization and linear least squares code for Program 3a have been posted.
4/18/24: 1. Homework 7 has been posted.
4/17/24: 1. Set 10 of the class notes on general linear least squares and the SVD have been posted. This is the last set of class notes.; 2. Date, time, location and rules for the Final Exam have been posted
4/12/24: 1. Some details about the definition of the SVD have been added to Set 9.
4/12/24: 1. The typo on the due date of Graded Homework 6 has been fixed. It is Friday April 19. Homework 7 will be posted before then so you are encouraged to complete a substantial part of Homework 6 before its due date so you can start on the last graded homework.
4/10/24: 1. Graded Homework 6 has been posted.
4/9/24: 1. Clarification and extra details on Givens rotations have been added to Set 8.
4/8/24: 1. Sets 8 and 9 of the class notes have been posted.
4/5/24: 1. Several papers on the symmetric eigenvalue problem, computing the SVD and specifically Jacobi's method have been posted.; 2. The solutions to Homework Set 5 have been posted.
4/3/24: 1. More details have been added to the immediate update Cholesky factorization fill-in generation and IC preconditioner in Set 6.
4/1/24: 1. The anonymous distribution for Graded Homework 2 has been posted.; 2. Program 4 has been posted for those pursuing the programming option.
3/27/24: 1. Hints for possible solution approaches have been added to Problems 1 and 2 in Graded Homework 5. As will all hints, these are not necessarily the only way to solve the problems.; 2. The choices for Program 3 given to those following the programming option have been posted for those following the written homework option wishing to see what was assigned.
3/26/24: 1. The solutions for Graded Homework 4 have been posted.; 2. Graded Homework 5 has been posted.
3/18/24: 1. The anonymous grade distribution for Graded Homework 1 has been posted.; 2. Set 7 of the class notes has been posted.
3/18/24: 1. A typo has been correct in Problem 5 of Graded Homework 4. The number of eigenvalues with the value μ₁ has been changed from k to s to avoid confusion with the index of the iteration.
3/14/24: 1. Graded Homework 4 has been posted.
3/14/24: 1. Detailed solutions for Graded Homework 3 have been posted.
3/4/24: 1. A request has been made to extend the due date slightly for Graded Homework 3. I have extended it until Monday March 11 at 11:59 PM.
2/29/24: 1. Graded Homework 3 has been posted.
2/28/24: 1. Notes on the steepest descent algorithm has been added to Set 6 of the class notes.
2/26/24: 1. Set 6 of the class notes has been posted.
2/21/24: 1. The solutions for the midterm exam havea been posted.
2/16/24: 1. A minor clarification was added to the orthogonal direct sum theorem's proof and Set 5 was reposted.
2/15/24: 1. The solutions to Homework 1 and Study Question Set 1 have been reposted with the addition of the classification of the problems into Basic, Intermediate, and Advanced for this course, as was done for Study Question Set 2. This should help you prepare for the midterm examination.; 2. The solutions for Homework 2 have been posted and have the classification of the problems into Basic, Intermediate and Advanced for this course.; 3. Note that the advanced question Problem 8 in Study Question Set 2 refers to Householder reflectors. These are covered in Set 5 on linear least squares problems. The question concerns in part an important difference between reflectors and Gauss transformations used in LU factorization that will be clear after Set 5. Clearly, you are not responsible for that part of the solution provided.; 4. Some reference surveys and the LAPACK User Manual have been posted. The latter gives information about the current standard numerical linear algebra library and has pointers to literature on algorithms and the BLAS. The other papers are from a range of years and concern parallel algorithms but also have detailed discussions of different versions of algorithms depending on the architecture as has been mentioned in lectures and class notes. These are for you reference and you are not required to read any for class this semester.
2/10/24: 1. The solutions to Study Questions Set 2 have been posted and, as requested, the levels of the questions relative to the class have been indicated.
2/9/24: 1. Comments on the solutions of Program 1 have been posted.

2. Set 5 of the class notes has been posted.

3. The data structure updates to compute the LU factorization using the delayed update version has been added to Set 3 of the class notes to give a clarifying example of the method's implementation.
2/7/24: 1. Set 4 of the class notes has been posted.

2. Study Question Set 2, Graded Homework 2 and Program 2 have been posted.

3. Matlab codes for the primitives and their testing from Program Assignment 1 have been posted.

4. Midterm Exam information has been posted. Follow the Exams button.
2/2/24: 1. A canvas announcement has been sent that may be helpful if you are experiencing some difficulties getting and accurate solution for larger sized triangular matrices with your program.
2/2/24: 1. Typos in Set 3 on slides 64 and 68 have been fixed and the set reposted.
1/31/24: There have been a few requests to extend the due date of Program 1 and I have examined the solutions that have been submitted. It is important that your solutions include the aspects described in the assignment. This includes systematic testing and a appropriate descriptions of why and how you generated your problems, what experiments you ran and why, and how your observations support the assertion that your codes work. The last part is important. When you run a large number of experiments, outputting the matrices and solution vectors is not a useful way of presenting the results to support your conclusions. So, I will extend the deadline until Monday at 11:59PM. Those who have already submitted a solution are free to update it and resubmit. There will be no further extension on this assignment.
1/31/24: 1. The code for one step of the partioned-algorithm on slide 43 of Set 3 has been corrected and the set reposted.
1/30/24: 1. The solutions for Graded Homework 1 have been posted.
1/29/24: The typo in the list of subroutines required has been fixed. (Old item 4 removed.) Two triangular solvers and two triangular matrix times a vector, and a matrix product M = L*U are all that are required.
1/26/24: The due date for Homework 1 is extended until Monday at 11:59PM. Those who have submitted solutions may, of course, update them if they wish. There will be no further extensions on this assignment.
1/25/24: 1. Set 3 on LU factorization has been substantially modified to include more detail. The set has been reposted.
1/24/24: 1. Program 1 has been posted.
1/23/24 1. Set 3 of the class notes has been modified with a new section and reposted. 2. Graded Homework 1 submission link has been added to Canvas.
1/22/24: 1. Set 3 of the class notes has been posted.

2. Graded Homework 1 due date is now 11:59 PM Friday January 26, 2024.
1/16/24: 1. Graded Homework 1 has been posted.
1/15/24: 1. Solutions for Study Question Set 1 have been posted.
1/12/24: 1. The definition of an eigenvalue, eigenvector pair has been added to the end of Set 1 of the class notes and the pdf file has been reposted.; 2. Study Question Set 1 has been posted.
1/10/24: 1. Set 2 of the class notes has been modified and reposted.
1/7/24: 1. The class syllabus has been posted.; 2. Sets 1 and 2 of the class notes have been posted.

Course Announcements

5/3/24

1. An anonymous semester point and grade distribution has been posted.

4/28/24

1. An anonymous grade distribution for Homework 7 has been posted.

4/27/24

1. Solutions for Homework 7 have been posted.

4/26/24

1. Typos in the solutions of problem 5.3(a) and 6.3(b) have been fixed and the solutions reposted.

4/23/24

1. The anonymous grade distribution have been posted for Homework 6 has been posted and the grades have been posted on Canvas.

4/23/24

1. Anonymous grade distributions have been posted for Homeworks 4 and 5 and the grades have been posted on Canvas.

2. The solutions for Homework 5 have been reloaded with a corrected solution for Problem 3.

4/20/24

1. Solutions for Homework 6 have been posted.

2. Information on the coverage of the Final Exam has been posted under the "Exams" button link.

3. Householder QR factorization and linear least squares code for Program 3a have been posted.

4/18/24

1. Homework 7 has been posted.

4/17/24

1. Set 10 of the class notes on general linear least squares and the SVD have been posted. This is the last set of class notes.

2. Date, time, location and rules for the Final Exam have been posted

4/12/24

1. Some details about the definition of the SVD have been added to Set 9.

4/12/24

1. The typo on the due date of Graded Homework 6 has been fixed. It is Friday April 19. Homework 7 will be posted before then so you are encouraged to complete a substantial part of Homework 6 before its due date so you can start on the last graded homework.

4/10/24

1. Graded Homework 6 has been posted.

4/9/24

1. Clarification and extra details on Givens rotations have been added to Set 8.

4/8/24

1. Sets 8 and 9 of the class notes have been posted.

4/5/24

1. Several papers on the symmetric eigenvalue problem, computing the SVD and specifically Jacobi's method have been posted.

2. The solutions to Homework Set 5 have been posted.

4/3/24

1. More details have been added to the immediate update Cholesky factorization fill-in generation and IC preconditioner in Set 6.

4/1/24

1. The anonymous distribution for Graded Homework 2 has been posted.

2. Program 4 has been posted for those pursuing the programming option.

3/27/24

1. Hints for possible solution approaches have been added to Problems 1 and 2 in Graded Homework 5. As will all hints, these are not necessarily the only way to solve the problems.

2. The choices for Program 3 given to those following the programming option have been posted for those following the written homework option wishing to see what was assigned.

3/26/24

1. The solutions for Graded Homework 4 have been posted.

2. Graded Homework 5 has been posted.

3/18/24

1. The anonymous grade distribution for Graded Homework 1 has been posted.

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

3/18/24

1. A typo has been correct in Problem 5 of Graded Homework 4. The number of eigenvalues with the value μ1 has been changed from k to s to avoid confusion with the index of the iteration.

3/14/24

1. Graded Homework 4 has been posted.

3/14/24

1. Detailed solutions for Graded Homework 3 have been posted.

3/4/24

1. A request has been made to extend the due date slightly for Graded Homework 3. I have extended it until Monday March 11 at 11:59 PM.

2/29/24

1. Graded Homework 3 has been posted.

2/28/24

1. Notes on the steepest descent algorithm has been added to Set 6 of the class notes.

2/26/24

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

2/21/24

1. The solutions for the midterm exam havea been posted.

2/16/24

1. A minor clarification was added to the orthogonal direct sum theorem's proof and Set 5 was reposted.

2/15/24

1. The solutions to Homework 1 and Study Question Set 1 have been reposted with the addition of the classification of the problems into Basic, Intermediate, and Advanced for this course, as was done for Study Question Set 2. This should help you prepare for the midterm examination.

2. The solutions for Homework 2 have been posted and have the classification of the problems into Basic, Intermediate and Advanced for this course.

2/10/24

1. The solutions to Study Questions Set 2 have been posted and, as requested, the levels of the questions relative to the class have been indicated.

2/9/24

1. Comments on the solutions of Program 1 have been posted.

2. Set 5 of the class notes has been posted.

3. The data structure updates to compute the LU factorization using the delayed update version has been added to Set 3 of the class notes to give a clarifying example of the method's implementation.

2/7/24

1. Set 4 of the class notes has been posted.

2. Study Question Set 2, Graded Homework 2 and Program 2 have been posted.

1. A typo has been correct in Problem 5 of Graded Homework 4. The number of eigenvalues with the value μ₁ has been changed from k to s to avoid confusion with the index of the iteration.