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CSE880 Computational Linear Algebra & Optimization
Campus
RCMS
Programs
PG
Session
Spring Semester 2017
Course Title
Computational Linear Algebra & Optimization
Course Code
CSE880
Credit Hours
30
PreRequisutes
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:
WellesleyCambridge 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