Date
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List of Topics or Sections in
Lectures
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Reading from Textbook [TB] or
Online
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Related Codes
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Assignment (Projects)
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Homeworks
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| Jan 13 |
MATLAB
Tutorial (Slide)
Cheat-Sheet
(Handout)
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Another
Short MATLAB Tutorial (html)
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Try
through Cheat-Sheet
Program B.1 (bounce.m) |
Project 1 (Due Jan 27)
Sorting
Algorithms: Bubble
Sort
BBsort.m ProblemA.m
Control Round-off
Errors
ProblemB.m
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MATLAB
Onramp
(Due Feb 5)
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| Jan 15 |
MATLAB Programming
Sec 0.1 Evaluating a Polynomial (Slide) |
[TB]
Sec 1.2 Fixed-Point Iteration
[TB] Sec 1.4 Newton’s
Method
[TB] Sec 1.5 Secant
Method
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Program 0.1 (nest.m)
Program 1.2 (fpi.m)
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Sec
0.1 #2, 6
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Jan 20
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MLK Day, No Class |
[TB] Appendix
A or Review Linear Algebra |
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Review
Sec 0.5
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Jan 22
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Sec 0.2 Binary Numbers
A Taste of Round-off Errors
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Famous
Software Bugs
Disasters caused by numerical errors
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Decimal to Binary Converter
SlideCodes
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Sec 0.2 #2,6,8
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Jan 27
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Sec 0.3
Floating Point Numbers |
Five
Tips for Floating Point Programming
IEEE
Standard 754
Floating-Point
Numbers in MATLAB
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Wilkinson polynomial (wilkpoly.m)
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Project
2 (Due Feb 10)
Thomas
algorithm : Thomas.m
Cholesky
factorization: Cholesky.m
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Sec 0.3
#4,6,14
Sec 0.4 #2,5,6
HW1 Due Feb 5 |
Jan 29
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Sec 0.4
Floating Point Operations |
Floating-Point
Arithmetic |
IEEE
754 Calculator
IEEE-754
Analysis |
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Feb 3
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Sec 2.1 Gaussian Elimination
Sec 2.2 LU Factorization |
Online
Slide 1
Online Slide
2
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GEsolver.m
(no pivoting)
GELU.m |
Overview
of GE |
Sec 2.1 #4
Sec 2.2 #4,5, CP#1
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Feb 5
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Sec 2.3 PA=LU Factorization
and |
Online
Slide 3
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PPGEsolver.m
(partial pivoting)
evil.m
(the matrix fails GE)
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Sec 2.3 #17,18
Sec 2.4 #7, 9
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Feb 10
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Sec 2.4
Condition number |
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Sparse
Matrices in MATLAB |
Project
3 (Due Feb 26)
Project3ProblemA.m
optimal
SOR method (paper)
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Sec 2.5 #2,
4
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Feb 12
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Sec 2.5
Iterative Methods for SPD matrices |
Online
Slide 4
Online
Slide 5
Finite Difference Laplacian in MATLAB
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Jac_GS_SOR_test.m
Program 2.1 (sparsesetup.m)
Program 2.2 (jacobi.m)
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Sec
2.6 #5(d), 6(b),
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Feb 17
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Sec 2.6 Preconditioners for SPD
matrices |
CG
Method (without pain), A
slide, Another
slide
CG
Explained (shorter but more math)
The
1952 CG paper (Cited by 8720)
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pcg_test.m
mycg.m
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Sec 2.6 #14(b)
HW2 Due Mar 4
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Feb 19
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Exam 1
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Feb 24
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Exam 1
Solution Session
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Feb 26
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Sec 2.6
Preconditioners for SPD matrices |
CG
Notes PCG
Notes
Online
Slide 6
Online Slide 7
History of iterative methods
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mypcg.m
mypcg_test.m
mypcgfun.m
mypcgfun_test.m
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Project
4 (Due Mar 25): comment
video
Project4ProblemA.m
(my code)
Preconditioning
techniques
Toeplitz
and Circulant Matrix
Strang's Preconditioner
paper
T. Chan's Preconditioner
paper
R. Chan's Preconditioner
paper
Super-optimal
preconditioner paper
Design
of more preconditioners
A
slide about FFT
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Mar 2
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Sec 4.1-4.2 Least Square
Models and Normal Equations
Sec 4.3 QR Factorization
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QR factorization slide 1
QR factorization slide 2
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Program 4.1 (clgs.m)
mgs.m (modified GS)
Program 4.2 (houseqr.m)
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Sec 4.1 #3, 12
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Mar 4
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Sec
4.3 QR Factorization |
A short
note comparing clgs and mgs
An Iteractive
Tool for demonstrating algorithms
A review
paper on Gram-Schmidt algorithms |
Example_4_5_test.m
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A
blog compared 3 QR algorithms
(its
updated_version, Bug is everywhere) |
Sec 4.3 #2,4,6,7
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| Mar 9-15 |
SPRING BREAK |
[TB] Chap 3 Interpolation
(skip theory)
[TB] Chap 6 ODEs (skip theory) |
Try
MATLAB
Interpolation functions
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Mar 16
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Sec 4.3 QR
Factorization
3 videos (with scanned
lecture notes)
QR (Classical
Gram-Schmidt Example 4.12)
Full
QR (Classical Gram-Schmidt Example 4.13)
Full
QR (Householder reflections, Example 4.19) |
Saddle-point
Systems
Toeplitz
Systems
The
original 1986 GMRES paper |
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Mar 18
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Sec 4.4
GMRES Method
2 videos (with scanned
lecture notes)
GMRES method video
based on this online notes
Arnoldi
Iteration video used within GMRES
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Arnoldi
Iteration and GMRES notes
More on Arnoldi
Iteration
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GMRESDemo.m
MATLAB's
gmres function
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Famous
Book: Iterative methods for Sparse Linear Systems |
Sec 4.4
#1(c)
HW3 Due Apr 1
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| Mar 23 |
Sec 5.1 Numerical Differentiation
(notes photo1,photo2)
Finite Difference
Formulas for 1st Derivative video
Finite Difference
Formulas for 2nd Derivative video
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Sec 5.1 #8, CP#1
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Mar 25
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Chap 6 Introduction to ODE IVP solvers (notes
photo)
Summary of ODE system
solvers video
Demo of how to use
ode45 solvers video
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Useful Notes Solve
ODE IVPs
Try MATLAB
ODE Examples
Try SIR
model or more
similar models |
ODEsolversDemo.m
Lorenz.m
SIRmodel.m
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Sec 6.5 p.347#2
Sec 6.6 p.350#2
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| Mar 30 |
Sec 7.1 Shooting Method for ODE BVPs (notes
photo)
Shooting method
explained video (first 10 min no sound)
Re-recorded
video for the first 10 mins |
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BVP_shootingmethod_test.m
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Project 5
(Due Apr 27): comment
video
Geometric
Multigrid method (codes)
A
tutorial book (only Chap 1- 3) ,
A
tutorial slide 1; A
tutorial slide 2
A
shorter slide
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Sec 7.1 CP #4,#5
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| Apr 1 |
Sec 7.2 Finite Difference Methods for ODE BVPs
Finite difference
method explained video (notes1,notes2)
understand this code: BVP_FDM_livescript.html
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A good
online video on
1D finite difference method
A slide for more
finite difference formulas
A
lecture Youtube video by Prof.
Wen Shen (PSU) |
BVP_FDM_livescript.mlx
(matlab)
BVP_FDM_livescript.html
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Sec 7.2 CP#1,#5
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| Apr 6 |
Sec 7.2 Introduction to 1D Multigrid
solvers
Following this
lecture video, study the marked
slide
understand 1D MG code (from SecondFD1dMG.m): BVP_FDM_GMG_livescript.html
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Tutorial Multigrid
Codes (start with the 1D
case)
More Multigrid
Codes
A long multigrid lecture notes
A
A short multigrid lecture notes
B
A
short note on multgrid method
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My 1D MG: SecondFD1dMG.m
BVP_FDM_GMG_livescript.mlx
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Another Classical
MG Book
A
short tutorial on multigrid method
An old website
for multigrid method
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| Apr 8 |
Sec 8.3 Elliptic Equations (2D
Poisson Equation)
Watch this video1,
video2
Understand
this slide, and reproduce the example codes
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A good
online video on
2D finite difference method |
Program 8.5 (poisson.m) |
2D FDM for Poisson PDE video
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Sec 8.3 #4, CP#4 |
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| Apr 13 |
Sec 8.3 Elliptic Equations (2D Multigrid solvers)
Watch 2D Multigrid video1
video2
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Another Poisson Multigrid
Codes
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My 2D MG: SecondFD2dMG.m |
The idea of multigrid lecture video
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| Apr 15 |
Exam 2 (cover lectures from Feb
17 to Apr 1)
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| Apr 20 |
Sec 8.1 Parabolic Equations
Watch this video
(first 55min) with hand-written
notes
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Program 8.1 (heatfd.m)
Program 8.2 (heatbd.m)
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Sec 8.1: #2, CP#2,3
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| Apr 22 |
Sec 8.1 Parabolic Equations
Watch this video
(last 35min) with hand-written
notes |
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Program 8.3 (heatbdn.m)
Program 8.4 (crank.m) |
Bonus Project (Due May 5)
Write 3-pages summary of AMG
paper
Algebraic Multgrid (codes)
A
video with slide
A
good slide; Another
slide
A review
paper 1; A review
paper 2
An
old AMG matlab codes
A longer AMG
slide
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| Apr 27 |
Sec 8.2 Hyperbolic Equations
Watch this video
with hand-written
notes |
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wavecd.m
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Sec 8.2: #2, CP#2
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| Apr 29 |
Review Lecture
Watch this video
with hand-written
notes |
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| May 4 |
Final Exam (Monday, May 4;
12:00pm-1:40pm)
To be open at 11am, due at 3pm (on Blackboard)
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