Numerical Methods G22.2420 Identical to G63.2010. Corequisite: G63.2110 (Linear Algebra). 3 points.
Linear algebra: matrix factorizations (LU, Cholesky, QR), condition number and numerical stability, matrix eigenvalue problem (Schur and SVD canonical form, QR and Toda algorithms), error analysis, modern hardware and software. Approximation: interpolation, splines, least squares. Integration: panel methods, extrapolation, Gauss quadrature. Nonlinear equations and optimization.
Advanced Numerical Methods G22.2421 Identical to G63.2020. Prerequisite: G22.2420. 3 points.
Ordinary differential equations: linear multistep methods, stability of difference equations, error bounds, boundary value problems. Elliptic equations: finite element method, variational principles, Ritz and Gallerkin approximations. Iterative solution of large sparse systems of equations: classical iterations, conjugate gradients, fast solvers, multigrid methods. Parabolic and hyperbolic equations.
Linear Programming G22.2730 Identical to G63.2741. Prerequisite: knowledge of linear algebra and FORTRAN. 3 points.
Formulation of linear programming problems. Convex sets and linear inequalities, duality. The simplex method. Computational and programming aspects of the simplex method, sparsity, data structures, and numerical stability. Applications to operations research and network problems. Software for linear programming.
Topics in Numerical Analysis G22.2945 May be identical to G63.2030, G63.2031, G63.2040, G63.2051, G63.2060. Prerequisites vary according to topic. 3 points.
Recent topics have included computational fluid dynamics, finite elements method, particle methods. Current course descriptions are available from the graduate office.
GSAS /
NYU
-- last modified 24 September 1996