Lecture materials
Before even the first class, I recommend that you refresh your linear algebra, for example, using these notes by Jonathan Goodman.Also get a CIMS computer account and start playing with MATLAB, for example, by looking at chapter 2 in the textbook by Greenbaum and Chartier, which I will refer to as "the textbook" below.
1 and 2. (Sept 3rd and 10th) Numerical Computing
For additional information look at chapters 5 and 6 in the textbook and chapter I in notes by Jonathan Goodman. See also part I (chapters 1-4) in the textbook by O'Leary.Here are some MATLAB scripts used as examples in the lecture notes: fibb.m, vect.m, Integral.m, harmonic.m (double precision) and harmonicSP.m (single precision). Also an example solution to the example homework problem: FirstDeriv.m and FirstDerivSP.m
3 and 4. (Sept 17th and 24th) Solving Linear
Systems
Here is the MATLAB code for MyLU.mFor dense square and overdetermined systems see chapter 7 in textbook, while for sparse matrices see 12.2 in the textbook. For a more in-depth overview of sparse solvers see chapters 27 (direct) or 28 (iterative) in the textbook by O'Leary.
For a more mathematical review of linear algebra consult these these notes by Jonathan Goodman, and for a more in-depth discussion on performance consult these notes by Jonathan Goodman.
5. (Oct 1st) Eigen
and Singular Values
Look at 12.1 in the textbook for eigenvalues; Google's
original Page Rank algorithm is covered in 12.1.5 and you may
find it interesting. Also see section 5.5 for eigenvalues and
5.6 for SVD in the textbook by
O'Leary.Here are some MATLAB scripts used as examples in the lecture notes: Compression.m.
6. (Oct 8th) Solving Nonlinear
Equations
Systems of nonlinear equations are not covered in the
textbook; see instead chapter 24 in the textbook by
O'Leary, and in particular the discussion of
continuation methods.Here are some MATLAB scripts used as examples in the lecture notes: FZero.m.
7. (Oct 15th) Optimization
Based on various sources, including these notes
by
Jonathan Goodman. Optimization is discussed in good
detail in chapters 9 (unconstrained) and 10 (constrained,
advanced) in the textbook by
O'Leary.Here are some MATLAB scripts used as examples in the lecture notes: Rosenbrock.m.
8. (Oct 22nd) Interpolation
See chapter 8 of textbook and also these notes by Jonathan Goodman.Here are some MATLAB scripts used as examples in the lecture notes: Runge1D.m, Hills2D.m, HillsIrreg2D.m.
9. (Oct 29th) Fast Fourier Transform
We will discuss Fourier Transforms, including the FFT algorithm, and briefly introduces wavelets.This is not covered in the textbooks.