MATH 170A: Numerical Linear Algebra
Fall 2008

Instruction

Instructor: Prof. Jiawang Nie

Office: AP&M 5864.

Phone: (805) 534-6015.

Email: njw "AT" math.ucsd.edu.

Office hours: 1:30 pm - 2:30 pm, Mondays, and 10:30 am - 11:30 pm, Wednesdays.

Lectures

Time: 12:00 noon - 12:50 pm, Mondays, Wednesdays, and Fridays

Location: Center Hall 222.

Course Description

Matrix-vector operations, positive definite matrices and Cholesky factorization, Condition Number, Perturbation Theory of Linear Equations, Floating Point Arithmetic, Stability of Algorithms, LU Decomposition--Gaussian Elimination, Partial Pivoting, Least Squares, Rotation and Relection matrices, QR factorization, Singulvar Value Decomposition , Eigensystems, Power Method, Hessenberge and tridiagonal forms, sensitivity of eigenvalues and eigenvectors.

See the tentative course syllabus.

Prerequisite

MATH 20F: Linear Algebra

Textbook

David S. Watkins, Fundamentals of Matrix Computations, 2nd edition, Wiley-Interscience, 2002.

Discussion Sessions and Teaching Assistant

Session A01: 6:00pm-6:50pm, HSS 1305, Dr. Hieu Nguyen

Session A02: 7:00pm-7:50pm, HSS 1305, Dr. Hieu Nguyen

Grader

Hieu Nguyen

Class Web Page

http://www.math.ucsd.edu/~njw/Teaching/Math170A_Fa08/math170A-fa08.html

Homework

Homework will be assigned in Wednesday's lectures and collected in the following Wednesday's lecture.

Homework #1: due on 10/08/2008
    Exer. 1.1.20,1.2.5,1.3.23,1.3.29, 1.4.22, 1.4.56, 1.4.58   (solution)

Homework #2: due on 10/15/2008
    Exer. 2.1.14, 2.1.17, 2.1.23, 2.1.31, 2.1.32, 2.2.6, 2.2.23   (solution)

Homework #3: due on 10/22/2008
    Exer. 2.3.12, 2.3.13, 2.5.4, 2.5.6, 1.7.10, 1.7.18   (solution)

Homework #4: due on 10/29/2008
    Exer. 1.7.32, 1.7.34, 1.7.44, 1.7.45, 1.7.50 (do (a),(b),(c) and (d), skip (e)), 1.8.4, 1.8.7   (solution)

Homework #5: due on 11/05/2008
    Exer. 3.2.3, 3.2.8, 3.2.12, 3.2.16, 3.2.17, 3.2.27, 3.2.47, 3.2.48   (solution)

Homework #6: due on 11/12/2008
    Exer. 3.3.4, 3.3.7, 3.4.4, 3.4.5, 3.4.22, 4.1.6, 4.1.13, 4.1.15

Homework #7

due on 11/19/2008
    Exer. 4.2.3, 4.2.10, 4.2.12, 4.3.8, 4.3.9, 4.3.11, 5.2.8, 5.2.14

Homework #8: due on 11/26/2008
    5.2.21, 5.2.23(a),5.3.8, 5.3.9, 5.4.7, 5.4.8, 5.4.17, 5.4.20,

Homework #9: Optional
    5.9.8, 5.9.9, 5.9.15, 5.9.18, 6.5.7, 6.5.13, 6.5.14, 6.5.26

Notes: (1) Please write your names, id nubmers, and section numbers on your homework. Please stable together your homework pages.

(2) no late homework will be accepted unless a written verification of a valid excuse (such as hospitalization, family emergency, religious observance, court appearance, etc.) is provided.

Computer Assignment

Computer assignment via MATLAB is required for this course.
Computer Lab with MATLAB is provided in AP&M building.

Computer Assignment #1: due on 10/08/2008
    Exer. 1.1.9, 1.1.10

Computer Assignment #2: due on 10/15/2008
    Exer. 1.4.16 (write a Matlab code)

Computer Assignment #3: due on 11/05/2008
    Exer. 1.8.12 (write a Matlab code)

Computer Assignment #4: due on 11/12/2008
    Exer. 3.3.10

Computer Assignment #5: due on 11/26/2008
    Write a MATLAB code to implement Classical Gram-Schmidt Algorithm (3.4.19) on Page 227. Requirements:
    Input: an arbitrary n-by-m matrix A
    Output: An n-by-m isometric matrix Q and an m-by-m upper triangular matrix R such that A = Q*R.

Here is a note on how to get started with MatLab.

Exams

There will be two midterms and one final.

Grading

The final course grade will be determined based on the assignments and exams with the weights:
Regularl homework - 20%, Computer Assignment - 10%, midterm exam 1 - 20%, midterm exam 2 - 20%, and the final exam - 30%.
The grades will be curved within the entire class.

Academic Integrity

Every student is expected to conduct themselves with academic integrity. Violations of academic integrity will be treated seriously.
See http://www-senate.ucsd.edu/manual/Appendices/app2.htm for UCSD Policy on Integrity of Scholarship.