Lecture site:  AP&M 2402 
Lecture times:  Monday, Wednesday, Friday. 2:00pm2:50pm. 
Final Exam time and place 
December 12th, 2018, 3:00pm  5:59pm. Place to be announced. 
Instructor 
Martin Licht
Email: mlicht AT ucsd DOT edu Office: AP&M 5880E Hours: Wednesdays, 1:00pm1:50pm. 
Grader 
Minxin Zhang
Email: miz151 AT ucsd DOT edu Office Hours: Thursdays 3:305:30 in AP&M 6446 
Section  949162 
Credit Hours:  4 units 
Course content  Error analysis of the numerical solution of linear equations and least squares problems for the full rank and rank deficient cases. Error analysis of numerical methods for eigenvalue problems and singular value problems. Iterative methods for large sparse systems of linear equations. Prerequisites: graduate standing or consent of instructor. 
Formal prerequesite  Graduate standing or consent of instructor. 
Homework  Homework will announced on every other Friday after lecture. Homework can be submitted to the mailboxes on every other Fridays before 2pm in the afternoon (before the lecture starts). All submissions must be in handedin in handwritten form. 
Grading  The final grade will composed by 50% of the homework and by 50% of the final exam. 
Academic Integrity  Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously. See http://wwwsenate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship. 
Textbook resources 
The following textbooks are recommended to supplement the lectures:

Additional Resources 
A collection of notes and articles that supplement the course content:

Helpful Links 
Lecture  Content 

# 1, 0F 28.09.2018. 
Administrative. Outline of Numerical Linear Algebra. I.1: Simple algorithms. Homework 1 announced. Intro Slides 
# 2, 1M 01.10.2018. 
I.2: Solving triangular systems of equations. 
# 3, 1W 03.10.2018. 
I.3: Inverting triangular matrices. I.4: LU decomposition. 
# 4, 1F 05.10.2018. 
I.4: LU decomposition, continued. 
# 5, 2M 08.10.2018. 
I.5: LU decomposition with pivoting. 
# 6, 2W 10.10.2018. 
I.5: LU decomposition with pivoting, Diagonally dominant matrices. 
# 7, 2F 12.10.2018. 
I.6: LDLT decomposition. SPD matrices. Homework 1 collected. Homework 2 announced. 
# 8, 3M 15.10.2018. 
I.7: Cholesky factorization. II.1: QR decomposition. 
# 9, 3W 17.10.2018. 
II.2: GramSchmidt orthogonalization. 
# 10, 3F 19.10.2018. 
II.3: QR decomposition using Givens rotations. 
#11, 4M 22.10.2018. 
II.3: QR decomposition using Givens rotations. II.4: QR decomposition using Householder reflections. 
#12, 4W 24.10.2018. 
II.5: LeastSquares Problems of Full Rank. 
#13, 4F 26.10.2018. 
II.5: LeastSquares Problems of Full Rank. Homework 2 collected. Homework 3 announced. 
26.10.2018: Deadline to change grading option, change units, and drop classes without "W" grade on transcript.  
#14, 5M 29.10.2018. 
III.1 LeastSquares Problems and their solvability. III.2 LeastSquares Problems and the Pseudoinverse. 
#15, 5W 31.10.2018. 
III.3 Schur decomposition and Singular Value Decomposition. 
#16, 5F 02.11.2018. 
III.3 Singular Value Decomposition and Pseudoinverse 
#17, 6M 05.11.2018. 
III.3 Direct Methods recapitulated. Direct Method Slides IV.1: Banach fixpoint theorem 
#18, 6W 07.11.2018. 
IV.2: Classical iterative methods via fixpoint theory, Spectral radius, and Convergence theory. 
#19, 6F 09.11.2018. 
IV.3: Gerschgorin circle theorem. Convergence of classical Richardson iteration. Homework 3 collected. Homework 4 announced. 
#20, 7M 12.11.2018. 
Veteran's Day Holiday 
#21, 7W 14.11.2018. 
IV.4: Jacobi method and GaussSeidel method. 
#22, 7F 16.11.2018. 
IV.5: Overrelaxation methods. 
#23, 8M 19.11.2018. 
V.1: Gradient descent and its convergence. 
#24, 8W 21.11.2018. 
V.1: Gradient descent and its convergence. 
#25, 8F 23.11.2018. 
Thanksgiving Holiday 
#26, 9M 26.11.2018. 
V.2: Method of Conjugate Gradients. Homework 4 collected. Homework 5 announced. 
#27, 9W 28.11.2018. 
V.2: Method of Conjugate Gradients. 
#28, 9F 30.11.2018. 
VI.1 Eigenvalue Problems via Power Iteration 
30.11.2018: Deadline to with "W" grade on transcript.  
#29,10M 03.12.2018. 
VI.1 Eigenvalue Problems via Inverse Iteration 
#30,10W 05.12.2018. 
VI.1 Eigenvalue Problems via QR algorithm. 
#31,10F 07.12.2018. 
Recapitulation of material. 
FI 12.12.2018. 
Final Exam. 3:00pm  5:59pm. APM 2402 