Date | Topic |
Handouts and other links |
Assigned Exercises |
Due Date |
9/6-9/9 |
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W |
Introduction: root-finding and computing tools | Tutorial for MATLAB (and its free clones) | For numerical answers, please give ~12 decimal places | |
Th |
1.1-1.2: Newton's method | Square root intro | 1.1 #6 1.2 #12abc |
Fri 9/16 |
F |
1.3 Fixed-Point Theorem | 1.3 #3 | Fri 9/16 | |
9/12-9/16 |
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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 |
9/19-9/23 |
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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 | |
9/26-9/30 |
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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 | |
10/3-10/7 |
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M |
2.7 Householder triangularization | 2.7 #6 (by hand) | Fri 10/14 | |
W |
2.8 Gram-schmidt | 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 Gauss-Siedel iteration | Example script for iteration methods | 3.1 #10 (give spectral radius for optimal w in SOR) | Fri 10/14 |
10/12-10/14 |
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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 |
10/17-10/21 |
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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 (take-home exam due Wed) | Solutions to some proof exercises | ||
F |
4.1 Lagrange interpolating polynomials | 4.1 #1, 2abcde | Fri 10/28 | |
10/24-10/28 |
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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 Newton-Cotes formulas | 5.1 #7a (choose n by trial and error to get error ~10e-6), #12ab (use n=100 and report error; compare f'' for a vs b) | Fri 11/4 | |
10/31-11/4 |
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M |
5.1 cont'd | Project info | ||
W |
5.2 Open Newton-Cotes 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 | |
11/7-11/11 |
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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 one-step methods | Euler's method function and example | 6.4 no problems assigned | |
Th |
6.5 Runge-Kutta 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 |
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F |
Review (take-home exam due Wed) | |||
11/14-11/18 |
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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 1e-8 | 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.^2-3*y.^2-y.^3 with residual error < 1e-8 | 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.^2-3*y.^2-y.^3 with residual error < 1e-8 | 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 1e-8) | Fri 12/2 |
11/19-11/27 | Thanksgiving break | |||
11/28-12/2 |
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M |
7.5 Direct search methods | 7.5 no problems assigned | ||
W |
No class | |||
Th |
No class | |||
F |
7.6 Nelder-Mead method | sortrows |
7.6 #8 (do 100 iterations, compare to actual min found using calculus) | Wed 12/7 |
12/5-12/9 | ||||
M |
7.7 Conjugate direction methods | 7.7 #7 | Wed 12/14 | |
W |
Finish chapter 7 | |||
Th |
Presentations | |||
F |
Presentations | |||
12/12-14 |
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M |
Presentations | |||
W | Presentations | |||
Final written reports due
12/19 |