MA/CSC
580: Numerical Analysis I
http://www2.ncsu.edu/eos/info/math/ma580_info/white/ma580hp.htm
This
site is being updated during the spring 2000 semester.
We will examine linear and nonlinear
methods that are very important in the numerical solution of differential
equations. Both the theory and implementation (via MATLAB) of these methods
will be emphasized. MA/CSC 580 is a
three credit course, and MA/CSC 591w is an optional one credit course. This one credit course will illustrate codes
for matrix products, explicit iterations, SOR methods, Gauss elimination,
conjugate gradient and GMRES methods.
Here coding will be in F90, MPI and OMP so that the IBM SP
multiprocessor can be used.
Time and
Place: MWF
8:05-8:55 in HA 366 for MA/CSC 580
F 9:10-10:00 in HA 269 for MA 591w
Instructor: R. E. White,
Professor of Mathematics, NCSU,
HA
308, 515-7478, white@math.ncsu.edu
Grading: Two hour
exams (50%) and homework (50%)
Prerequisites: Matrix
Algebra (eg. MA 405) and Advanced Calculus (eg. MA 511)
Course
Outline:
1.0
Introduction
computational science, floating point numbers
roundoff and accumulation errors, stability, application to
heat and mass transfer, computers
2.0
Linear, Ax = d, A is nxn and Direct Methods
Gaussian elimination, row interchanges and pivots, Schur
complement, symmetric, banded and ill-conditioned matrices
3.0
Linear, Ax = d, A is mxn with m ¹ n
least squares, normal equations, QR factorization methods,
multiple solutions and equilibrium equations
4.0
Eigenvalues, Ax = lx
approximation, power and Jacobi methods, QR algorithm and
application to Schrodinger equation
5.0
Linear, Ax = d, A is nxn and Iterative Methods via Splittings
Jacobi, SOR, block versions, convergence theory, P-regular
splittings, ADI, incomplete factorizations, residual correction
6.0
Linear, Ax = d, A is nxn and Iterative Methods via Minimization
steepest descent, conjugate gradient, preconditioners,
Krylov and GMRES(m)
7.0
Nonlinear, F(x) = 0
basic methods, variation of mean value theorem,
Picard method, Newton method and variations