MATH 92:564 . Numerical linear ALGEBRA [Mirie]
TEXTBOOK: Mathews and Fink Prentice Hall
Instructor Rida Mirie Olney 428D . PHONE: 978-934-Email. Rida_mirie@Uml.edu
Web-page http://faculty.uml.edu/rmirie/92.564
Office Hours: 5-6 PM Monday . .[830:9:20 AM MWF] ,[ 11:30-12:20AM MWF]
and by appointment.
(3 exams 1-final + HW 20% each).
Chapters (3, 9, and 11) Review elementary matrices and their properties. Special matrices such as symmetric, orthogonal. Inverse using determinants, Operations on matrices. Cayley-Hamilton
LU decompositions and solutions of triangular systems.
Gauss elimination. Eigen-values and eigen-vectors (diagonalization of symmetric matrices)
Simultaneous diagonalization. Gaussian eliminations, matrix factorizations( LU-decompositions)
Power method, the inverse power method.
QR-factorization
Hesenberg matrices,. The QR algorithm.
Linear least square Problem
Singular value Decomposition(SVD) least square problems.
Iterative methods in solving AX=B, Jacobi, Gauss-Seidel methods.
Basic method convergence, The successive over relaxation (SOR)
The conjugate gradient method.
Applications : Gramm-Schmidt orthogonalization,
Numerical solutions for ordinary differential equations [initial value problems and BVP].
Numerical solutions of partial differential equations
[heat, wave and laplace] band matrices and the solution of linear band systems.