Math
441: Numerical Linear Algebra and Optimization
| Instructor |
Mark
Pernarowski |
| Textbook |
Numerical
Mathematics and Computing, 6th
edition |
|
Cheney and Kincaid
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| Office
Hours |
Schedule
(Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
Wil
1-115 |
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Grading: The course % for M441 is determined by:
Midterm M 100 Final F 100 Homework HW 200 _______________________________ 400 % = (M+F+HW)/4
The final is not comprehensive and both the final and midterm are take home exams.
Homework and exam due dates will be announced in class and posted here at a later date. Exam content will be announced in class.
Midterm and Final due dates and details will be announced in class.
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Syllabus: Material for M441 will be selected from: Chapter 1 Introduction and Taylor Series Review Chapter 2 Computer Arithmetic Chapter 3 Roots of Nonlinear Equations Chapter 7 Solution Methods for Linear Systems Chapter 8 Factorization and Iterative Techniques Chapter 12 Data Smoothing and Least Squares Chapter 16 Minimization of Functions
Material from these textbook sections will be covered in much greater detail in class. Notes will be posted below. PDF of Syllabi
Homework: Assigned homework and some of their solutions will be posted below as the course develops.
Homework scores will vary depending on their length and difficulty. The raw scores will be summed, and converted into a % to yield the 200 points in the final grade.
Computing: You will be given a computer account so you may use "matlab" to explore and implement some of the methods described in class. There might be computer based HW but I have not yet decided.
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Homework
and Exams for M441:
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Due
Date
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Content |
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| Homework 1 |
Sept 16 |
M441 |
Error Bounds,
Taylor series |
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| Homework 2 |
Sept
30 |
M441 |
Error
Analysis in Bisection/Newton
methods |
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| Homework 3 |
Oct
12 |
M441 |
Taylor
Series, Error Analysis, Newton
and other Methods |
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| Midterm
1 |
Oct
21 |
M441 |
on
HW 1 and 3 (errata on 4b -new X0
vector ) |
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| Homework 4 |
Nov
4 |
M441 |
Gauss
Elim, Matrix Decomp, Loss of
Sig., Block systems |
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| Homework
5 |
Nov 30 |
M441 |
Norms, Iterative methods |
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| Take
Home Final |
Dec 14 |
M441 |
everything since Midterm 1 |
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Classnotes: Updated 12/09
The following topics are all in a
single
PDF file --------- here
- Introductory
definitions, concepts
- Horner's
method
- Taylor
Series
- Bisection
Method
- Newton's
Method 1-D
- Newton's
Method 2-D
- Newton's
Method Convergence
- Newton's
Method Complex
- Secant
Method
Further note postings (not typeset):
- Matrix
notations and computational complexity
- Gaussian
elimination, LU-decomposition,
Scaled Partial Pivotting
- Other
Matrix Factorizations: LDU, PLU,
LDLT,
LLT
(Cholesky)
- Block
and tridiagonal systems
- Vector and
matrix norms, errors, condition number
- Iterative
Technique - General Theory; Richardson, Jacobi, Gauss-Seidel
- Iterative
Technique - More on convergence criteria, Neumann Series
- Iterative
Technique - Steepest Decent
- Iterative
Techniques - Conjugate Gradient
- Power method
for Eigenvalues
- Least
Squares Solutions - basics
- Nonlinear
Optimization
Computer Labs:
- Introduction
to Matlab: Bisection Method (Horner.m
Bisect.m
and f.m
)
- (Sept
23) Basic
matlab, Bisection, convergence,
linear convergence
- Download Basic.m
read and follow directions
- Download new version of Bisect.m
. Read and try to understand what
minor modifications were made with special not on the output
[xxxxx,yyyyy] format.
- Modify
your f.m file so f(x) = x.^2-4.
- Download Bisect_Error.m
-- execute the
code, read the comment lines and do as directed.
- Download NewtonPlot.m
--- read, execute
and modify as instructed for f(x)=x.^2-4
- Download Newton.m
-- read,modify and execute
- (Sept
28) Bisection and Newton's Method
------ (IS A HOMEWORK ASSIGNEMENT ABOVE)
- Download Bisect_Error.m
-- this is
slightly modified from the last day's version. Read it carefully and
alter the code to create the figures requested. You will also learn how
to create printable "postscript" files of the figures. You will create
2 figures in Project 3. The first two projects I coded and will work
with minor modifications.
- Download Newton.m
--- read, execute
and modify as instructed for the functions described. You will create 2
figures here regarding the convergence for two different functions.
- Download Newton_more.m
-- read, execute and modify. Should have 2 figures in end.
- (Nov
18 - possibly) Some scratch
code for now
- Basic
Matrix calculations
- Jacobi
and oher iterations
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