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CY902 Computational Linear Algebra and Optimization

Previous Lecturer:

David White

Course Homepage:

Academic Year 2010

This course is NOT running in academic year 2014-15

Please see CY902N

  • To familiarise students with the techniques of Computational Linear Algebra.
  • Understand the performance issue associated with Computational Linear Algebra.
  • Familiarise students with standard Linear Algebra Libraries.
  • Learn to formulate problems in terms of Linear Algebra operations.
  • To introduce the central mathematical ideas behind algorithms for the numerical solution of Optimization problems.
  • To provide theoretical justification for various algorithms and to outline basic issues of numerical analysis involved in Optimization problems.
  • To present key methods for both constrained and unconstrained Optimization.
  • To learn about available implementations and software packages.
  • To learn about various heuristic strategies used in science and engineering applications, in particular for global Optimization.

Learning Outcomes:

  • Use standard techniques of Computational Linear Algebra.
  • Use standard software for Computational Linear Algebra.
  • Formulate Scientific Computing problems as Linear Algebra Operations.
  • Understand the Mathematical background to solving Numerical Optimization problems.
  • Understand and use methods for constrained and unconstrained Optimization.
  • Demonstrate familiarity with standard software package for Optimization.

Prerequisites:

  • A good working knowledge of a scientific programming language (as for example taught in PX270 C Programming).
  • A background in Linear Algebra (as taught in MA251).
  • Some knowledge of Vector Calculus (as taught in MA231).

Syllabus:


  1. Linear Algebra in Computational Science
  2. Computer Architecture and Linear Algebra
  3. Revision of Linear Algebra
  4. Basic Linear Algebra routines
  5. Small matrix eigenvalue problem and linear equations
  6. Large matrix eigenvalue problems and linear equations
  7. Singular Value Decomposition
  8. Programming techniques in Linear Algebra
  9. Mathematical Introduction to Optimization
  10. Optimality Conditions
  11. Unconstrained Optimization Algorithms
  12. Computational Issues
  13. Global Optimization
  14. Constrained Optimization Algorithms
  15. Optimal Control and Dynamic Programming
  16. More Computational Issues