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Math 441: Numerical Linear Algebra and Optimization 


 
Instructor Mark Pernarowski 
Textbook Numerical Mathematics and Computing, 6th edition
Cheney and Kincaid
Office Hours Schedule (Wil 2-236)
Phone 994-5356
Classroom Wil 1-115   

Math 441

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Homework/Exams  Classnotes/Handouts  Computer Labs

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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.









 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:



 
Due Date
Content  .
 
Homework 1 Sept 16 M441 Error Bounds, Taylor series  
Homework 2 Sept 30 M441 Error Analysis in Bisection/Newton methods
Homework 3 Oct 12 M441 Taylor Series, Error Analysis, Newton and other Methods
Midterm 1 Oct 21 M441 on HW 1 and 3 (errata on 4b -new X0 vector )
Homework 4 Nov 4 M441 Gauss Elim, Matrix Decomp, Loss of Sig., Block systems
Homework 5 Nov 30 M441 Norms, Iterative methods
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
  1. Introductory definitions, concepts
  2. Horner's method
  3. Taylor Series
  4. Bisection Method
  5. Newton's Method 1-D
  6. Newton's Method 2-D
  7. Newton's Method Convergence
  8. Newton's Method Complex
  9. Secant Method
Further note postings (not typeset):
  1. Matrix notations and computational complexity
  2. Gaussian elimination, LU-decomposition, Scaled Partial Pivotting
  3. Other Matrix Factorizations: LDU, PLU, LDLT, LLT (Cholesky)
  4. Block and tridiagonal systems
  5. Vector and matrix norms, errors, condition number
  6. Iterative Technique - General Theory; Richardson, Jacobi, Gauss-Seidel
  7. Iterative Technique - More on convergence criteria, Neumann Series
  8. Iterative Technique - Steepest Decent
  9. Iterative Techniques - Conjugate Gradient
  10. Power method for Eigenvalues
  11. Least Squares Solutions - basics
  12. Nonlinear Optimization






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Computer Labs:


  1. Introduction to Matlab: Bisection Method (Horner.m  Bisect.m and f.m
  2. (Sept 23) Basic matlab, Bisection, convergence, linear convergence
    1. Download Basic.m read and follow directions
    2. 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.
    3. Modify your f.m file so f(x) = x.^2-4.
    4. Download Bisect_Error.m  -- execute the code, read the comment lines and do as directed.
    5. Download NewtonPlot.m  --- read, execute and modify as instructed for f(x)=x.^2-4
    6. Download Newton.m   -- read,modify and execute
  3. (Sept 28) Bisection and Newton's Method   ------ (IS A HOMEWORK ASSIGNEMENT ABOVE)
    1. 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.
    2. 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.
    3. Download Newton_more.m   -- read, execute and modify. Should have 2 figures in end.
  4. (Nov 18 - possibly)  Some scratch code for now 
    1. Basic Matrix calculations
    2. Jacobi and oher iterations






 
 
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View Text-only Version Text-only Updated: 12/09/2010
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