MATH 581
Numerical Methods for Linear Systems

Fall 2011




syllabus and notes



Below is a tentative schedule of lectures. Schedule and topics are subject to change (probably not much)


 

topics

week 1 (08/29 - 09/02)

matrix-vector multiplication, orthogonal vectors and matrices

week 2 (09/06 - 09)

norms, the Singular Value Decomposition

week 3 (09/12 - 16)

projectors, QR factorization

week 4 (09/19 - 23)

Gram-Schmidt orthogonalization, householder triangularization, least squares problems

week 5 (09/26 - 30)

Gaussian elimination, pivoting

week 6 (10/03 - 07)

stability of Gaussian elimination, Cholesky factorization

week 7 (10/10 - 14)

eigenvalue problems, reduction of Hessenberg or tridiagonal form

week 8 (10/17 - 21)

midterm review, MT exam

week 9 (10/24 - 28)

Rayleigh quotient, inverse iteration

week 10 (10/31 - 11/04)

QR algorithm without shifts, QR algorithm with shifts

week 11 (11/07 - 11)

other eigenvalue algorithms, computing the SVD

week 12 (11/14 - 18)

overview of iterative methods, conjugate gradients, preconditioning

week 13 (11/21 - 23)

Jacobi iteration, Gauss-Siedel iteration

week 14 (11/28 - 12/02)

SOR, other methods for linear systems

week 15 (12/05 - 09)

final exam review, final exam




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