- 8/19/02: sec. 2.1 - Number representation. Additional information:
Michael Overton, Numerical Computing with IEEE Floating Point Arithmetic
Demonstration: display of representation of
numbers
- 8/21/02: sec. 2.1 - rounding errors
- 8/26/02: sec. 2.2, 2.3: loss of significance, relative error, backward error analysis,
condition (linear case)
homework 1 due 9/4/02
- 8/28/02 2.2,2.3 finish
- 9/2/02 Labor Day
- 9/4/02 - 2.3 condition (nonlinear case), unstable computations
- 9/9/02: sec. 3.1 - Bisection method, 3.2 - Newton's method, - hw2: 1. write program for the
Bisection method 3.1/computer 1, 2. write program for Newton's method in n dimensions
and run on examples 3.2/computer 14 3. 3.4/12 solution
- 9/11/02: sec. 3.4 - fixed points and functional iterations: Banach spaces, Banach contraction
theorem, linear case: matrix norm, nonlinear case: Mean-Value theorem in >1D, example: Newton's method,
quasi-Newton's method. See skeleton Matlab files for required format
- 9/16/02: sec. 3.4 banach contraction principle, secant method (no proof)
- 9/18/02: sec. 3.4 functional iterations and orders of convergence
- 9/23/02: sec. 3.5: Horner's rule hw3: 3.4/38,40 solution
- 9/25/02: Horner's rule and companion matrix
- 9/30/02: matrices, eigenvalues and eigenvectors hw4: 4.1/7,9,16; 4.2/computer 1
- 10/2/02: positive definite matrices (completion), block matrices, triangular matrices
- 10/7/02: Gauss elimination, elementary matrices, LU decomposition
- 10/9/02: LU decomposition (existence, block method), BLAS
- 10/14/02: review for midterm
- 10/16/02: midterm
- hw5: 4.2/23,25,25 4.3/computer 1
- hw6: 4.4/22 4.5/24 computer 3
- 11/25/02 hw7: 6.1/21,27(equidistant),37