National University of Sciences and Technology
Home | Back
CSE-880 Computational Linear Algebra & Optimization
Campus RCMS
Programs PG
Session Spring Semester 2017
Course Title Computational Linear Algebra & Optimization
Course Code CSE-880
Credit Hours 3-0
Course Objectives
  • To familiarize students with the techniques of Computational Linear Algebra.
  • Understand the performance issue associated with Computational Linear Algebra.
  • Familiarize 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.
Detail Content
  • Linear Algebra in Computational Science
  • Computer Architecture and Linear Algebra
  • Revision of Linear Algebra
  • Basic Linear Algebra routines
  • Matrix factorizations
  • Small matrix eigenvalue problem and linear equations
  • Large matrix eigenvalue problems and linear equations
  • Structured Matrices as well as iterative methods and least squares
  • Singular Value Decomposition
  • Programming techniques in Linear Algebra
  • Mathematical Introduction to Optimization
  • Optimality Conditions
  • Unconstrained Optimization Algorithms
  • Computational Issues
  • Global Optimization
  • Constrained Optimization Algorithms
  • Optimal Control and Dynamic Programming
  • Efficiency and stability of algorithms
  • Parallel techniques for solving linear and nonlinear equations
  • 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
  • Understand and use methods for constrained and unconstrained Optimization.
  • Demonstrate familiarity with standard software package for Optimization.
Text/Ref Books
  • Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA:
  • Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714.
  • Trefethen, Lloyd and Bau, David. Numerical Linear Algebra, SIAM, 1997
  • Nocedal, J. and Wright, S.
  • Numerical Optimization, Springer Verlag 1999
Time Schedule Spring Semester 2017
Faculty/Resource Person Dr Junaid Ahmad Khan
PhD (National University of Science and Technology (NUST)
Discipline: Computational Science & Engineering
Specialization: Computational Fluid Dynamics