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Numerical Linear Algebra

CS51500

Fall 2017

Days/Time: TTh / 10:30-11:45 am
Credit Hours: 3

Learning Objective:
At the end of the course, you should: understand the algorithms underlying matrix computations software for dense matrices, be able to implement basic versions of these algorithms, understand the difference between iterative methods for linear systems and direct methods, be able to implement iterative methods for large scale problems, appreciate the variety of applications of matrix computations. Students will:
a) become knowledgeable about major kernels and algorithms underlying matrix computations for dense and sparse matrices including linear systems of equation, symmetric eigenvalue problems, and the singular-value decomposition
b)be able to implement basic versions of these kernels and algorithms
c) learn the difference between direct and iterative methods for linear systems
d)gain expertise in the design of iterative methods and preconditioning techniques for large-scale sparse linear systems
e)be able to implement eigenvalue and singular-value problem solvers.

Description:
This course is an in-depth study of numerical linear algebra and the matrix computations that arise in solving linear systems, least squares problems, and eigenvalue problems for dense and sparse matrices. It will cover many of the fundamental algorithms such as the LU decomposition, the Cholesky decomposition, the conjugate gradient method, and the GMRES method. The course is designed for those who wish to use matrix computations in their own research and especially those in applied engineering and science.

Topics Covered:
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.

Prerequisites:
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.

This class is an in-depth graduate lecture class. You (the student) should have taken a mathematical course on linear algebra that covers vector spaces as well as a numerical analysis course that covers computer implementations of numerical algorithms.

Applied/Theory: 40/60

Web Address:
https://www.cs.purdue.edu/homes/dgleich/

Web Content:
Syllabus, schedule, readings, references, homework assignments, and message board. Piazza to support course

Homework:
Frequent quizzes and homeworks.

Exams:
One midterm and a final exam.

Textbooks:
Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
Tentative--Matrix Computations. Gene H. Golub and Charles van Loan. 4th Edition, Johns Hopkins University Press. Numerical Linear Algebra. Lloyd N. Trefethen and David Bau. ISBN: 9781421407944 SIAM.

Computer Requirements:
ProEd Minimum Computer Requirements. Instructor expects all assignments to be legible and well-written. For this, I require using a computer to prepare all submitted materials. In addition, there will be programming required for this class that will require the use of Matlab software or an equivalent.

ProEd Minimum Requirements: view

Tuition & Fees: view

Other Requirements:
The assignments will involve producing computer codes. These need to be documented and written in accordance with best software engineering practices. Failure to follow this advice may result in solutions receiving zero points. Moreover, these should be prepared individually.

SEMESTERS

Fall 2017
Fall 2019
Fall 2021

CURRENT INSTRUCTOR(S)

David Gleich

Phone
765-496-7300

Email
dgleich@purdue.edu

Office
Purdue University
Department of Computer Science
305 N. University Street
West Lafayette, IN 47907

Instructor HomePage