Lecture 1: 8/31/2006
A. Introduction
  1. Main topics of course
  2. I.E., main problems to be considered.


Lecture 2: 9/7/2006

A.General Techniques to be used throughout this course.
  1.Matrix Factorizations
    a.Gausian Elimination (A=PLU)
    b.Jordan Canonical Form (A=VJV^-1)
    c.Schur Factorization (A=UTU*)
  2.Peturbation Theory and Conditioning
    a.errors in input data to an algorithm
    b.Condition number
      -transfer an error bound on input data to an error bound on solution
      -absolute/relative condition numbers
  3.Effects of Roundoff Error
    a.errors caused by algorithm itself 
    b.forwards/backwards error
    c.backwards stability
  4.Speed of algorithms
    a.count flops (doesn't take into account moving data)
  5.Engineering/Numerical Software
    a.Issues
      -ease of use
      -reliability
      -speed
    b.3paradigms
      -software library (traditional)
      -commercial systems
      -templates

B.Floating Point Arithmetic

C.Polynomial Evaluation Example

Lecture 3: 9/14/2006

A.Vector and Matrix Norms
  0. Norm homework problems discussed
  1. p-norms infinity norm
  2. Matrix norms, max norm, Frobenius norm,  operator norms induced by vector
norm
  
Lecture 4: 9/21/2006
A. Perturbation theory for linear systems