Date  Topic 
Handouts and other links 
Assigned Exercises 
Due Date 
9/69/9 

W 
Introduction: rootfinding and computing tools  Tutorial for MATLAB (and its free clones)  For numerical answers, please give ~12 decimal places  
Th 
1.11.2: Newton's method  Square root intro  1.1 #6 1.2 #12abc 
Fri 9/16 
F 
1.3 FixedPoint Theorem  1.3 #3  Fri 9/16  
9/129/16 

M 
1.4 Convergence  Iterative method example  1.4 #4 (use function in example 1.4.2), 5ab  Wed 9/21 
W 
1.5 Variants  Newton's method as function Convergence order example 
1.5 #1  Wed 9/21 
Th 
1.6 Brent's method  Muller's method example  1.6 #1 (Muller's method), 15  Fri 9/23 
F 
1.7 Finite precision  Quadratic formula  1.7 #8ab (for Freemat use realmax=1.797693134862314*10^308)  Fri 9/23 
9/199/23 

M 
1.8 Newton's method for systems  Newton's method for systems function  1.8 #7, 10  Wed 9/28 
W 
1.9 Broyden's method  Broyden's method example  1.9 #3ab (use inverse of A1 for B1)  Wed 9/28 
Th 
2.1 Partial pivoting  2.1 #1a, 4abd (not c), 7abc  Fri 9/30  
F 
2.2 LU decomposition  2.2 #2ac, 3abc  Fri 9/30  
9/269/30 

M 
2.3 LU + pivoting  2.3 #2ab, 3, 9  Wed 10/5  
W 
2.4 Cholesky decomposition  2.4 #6ab (by hand), 7a, 9a  Wed 10/5  
Th 
2.5 Condition numbers  2.5 #3, 6, 8  Fri 10/7  
F 
2.6 QR decomposition  2.6 #1a, 4abcd  Fri 10/7  
10/310/7 

M 
2.7 Householder triangularization  2.7 #6 (by hand)  Fri 10/14  
W 
2.8 Gramschmidt  2.8 #2ac  Fri 10/14  
Th 
2.9 Singular value decomposition  2.9 #8 (use computer, not by hand)  Fri 10/14  
F 
3.1 Jacobi and GaussSiedel iteration  Example script for iteration methods  3.1 #10 (give spectral radius for optimal w in SOR)  Fri 10/14 
10/1210/14 

W  3.2 Sparsity (Mon class schedule) 
3.2 no problems assigned  
Th 
3.3 Iterative refinement  Iterative refinement example LU scripts 
3.3 #7  Thurs 10/20 
F 
3.4 Preconditioning  Preconditioning example  3.4 #7a  Thurs 10/20 
10/1710/21 

M 
3.5 Krylov space methods  GMRES example  3.5 #2 (4 iterations), 4a (add 5th row to A: 0 2 2 1 1, do 5 iterations)  Fri 10/28 
W 
3.6 Numerical eigenproblems  Power method and Hotelling's deflation example  3.6 #1ab, 10abcd  Fri 10/28 
Th 
Review (takehome exam due Wed)  Solutions to some proof exercises  
F 
4.1 Lagrange interpolating polynomials  4.1 #1, 2abcde  Fri 10/28  
10/2410/28 

M 
4.1, continued 
Polynomial examples  
W 
4.2 Piecewise linear interpolation  4.2 #1abc, 5 (for plots, can email as png)  Wed 11/2  
Th 
4.3 Cubic splines  Cubic spline example  4.3 #2, 5, 7 (typo in book's answer to #5)  Wed 11/2 
F 
5.1 Closed NewtonCotes formulas  5.1 #7a (choose n by trial and error to get error ~10e6), #12ab (use n=100 and report error; compare f'' for a vs b)  Fri 11/4  
10/3111/4 

M 
5.1 cont'd  Project info  
W 
5.2 Open NewtonCotes formulas  Adaptive Trapezoidal Rule  5.2 #7, 15a  Wed 11/9 
Th 
5.3 Gaussian quadrature 5.6 Adaptivity 
Mathematica examples  5.3 #1, 4, 8ad for only m=1, f(x)=sqrt(abs(x)), 4 point rule  Fri 11/11 
F 
6.1 Numerical differentiation  6.1 #1 (plot for x=1:0.05:2, rather than writing out values), 9 (want O(h^2) error)  Fri 11/11  
11/711/11 

M 
6.2 Euler's method 6.3 Improved Euler's method 
Euler's method example  Plot solutions on [0,1] for y'=2xy, y(0)=1 using h=0.1 and h=0.01 for Euler's method and improved Euler's method (along with the true solution). State error at x=1 for each case.  Fri 11/18 
W 
6.4 Analysis of onestep methods  Euler's method function and example  6.4 no problems assigned  
Th 
6.5 RungeKutta method 
Plot solutions on [0,1] for y'=2xy, y(0)=1 using h=0.1 and h=0.01 for RK4 (along with the true solution). State error at x=1 for each case. 
Fri 11/18 

F 
Review (takehome exam due Wed)  
11/1411/18 

M 
7.1 Nonlinear optimization  Golden section search method example  Use the golden search method to calculate the locations of all four local extrema of f(x)=x.^2.*sin(x)2*x on the interval [3,3] to within 1e8  Fri 12/2 
W 
7.2 Steepest descent  Golden section search fn for use in steepest descent Steepest descent example 
Use steepest descent with golden search to calculate the locations of the two minima of f(x)=8*y.^4+x.*y+x.^23*y.^2y.^3 with residual error < 1e8  Fri 12/2 
Th 
7.3 Newton methods  Newton's method fn  Use the Newton method with Hessian to calculate the locations of the two minima of f(x)=8*y.^4+x.*y+x.^23*y.^2y.^3 with residual error < 1e8  Fri 12/2 
F 
7.4 Multiple random start  Project topic due  Apply the MRS method to the Rastrigin function for d=2 on the region [5.12,5.12]x[5.12,5.12]. Run the method 20 times, each time using 100 random starts. How often does it find the true global min? (to within 1e8)  Fri 12/2 
11/1911/27  Thanksgiving break  
11/2812/2 

M 
7.5 Direct search methods  7.5 no problems assigned  
W 
No class  
Th 
No class  
F 
7.6 NelderMead method  sortrows 
7.6 #8 (do 100 iterations, compare to actual min found using calculus)  Wed 12/7 
12/512/9  
M 
7.7 Conjugate direction methods  7.7 #7  Wed 12/14  
W 
Finish chapter 7  
Th 
Presentations  
F 
Presentations  
12/1214 

M 
Presentations  
W  Presentations  
Final written reports due
12/19 