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Numerical Analysis II

782

Direct and iterative methods for solving systems of linear equations. Numerical solution of partial differential equations. Numerical determination of eigenvectors and eigenvalues. Solution of nonlinear equations.

Text: 

Numerical Linear Algebra, Trefethen and Bau III, SIAM, 1997.

Prerequisite: 

MATH 781 or instructor's permission.

Credit Hours: 
3

This is a sequel of MATH 781 concentrating on numerical linear algebra and optimization. One or two topics will be selected from each of the following units.

  1. Matrix factorizations for linear equations and least squares. Krylov subspace methods for linear equations and least squares.
  2. Error analysis and conditioning for linear equations and least squares.
  3. Unconstrained optimization in several variables including Newton and quasi-Newton methods with line search.
  4. Methods for the algebraic eigenvalue problem possibly including Jacobi and QR iterations, Krylov subspace methods, and divide & conquer.
  5. Methods for partial differential equations.
  6. An additional unit suggested by and of special interest to the class.
Frequency: 
Every Spring Semester

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