CS51500 - Numerical Linear AlgebraFall 2017
Days/Time: TBD / TBD
Credit Hours: 3
Direct and iterative solvers of dense and sparse linear systems of equations, numerical schemes for handling symmetric algebraic eigenvalue problems, and the singular-value decomposition and its applications in linear least squares problems.
Dense Matrix Computation: Direct linear system solvers; LU and Cholesky factorization schemes, Norms and condition numbers, Pivoting strategies, scaling, and iterative refinement. Least squares problems; Orthogonal projections, Orthogonal factorization schemes--Givens, Householder, and Gram-Schmidt, Singular-value decomposition. The symmetric eigenvalue problem; Eigenvalues and eigenvectors, Power method and inverse iteration, Reduction to the tridiagonal form, Extraction of eigenpairs. Iterative methods for sparse linear systems: Discretization of partial differential equations, Sparse matrices, Basic iterative linear system solvers, Projection methods, Krylov subspace methods, Schemes for normal equations, Preconditioning techniques.
A bachelor degree in computer science or an equivalent field. Students not in the Computer Science master's program should seek department permission to register.
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