Numerical Linear Algebra (MDES621) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Linear Algebra MDES621 Elective Courses 3 0 0 3 5
Pre-requisite Course(s)
MATH 275 Linear Algebra or equivalent
Course Language English
Course Type Elective Courses
Course Level Natural & Applied Sciences Master's Degree
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives This course is designed to give engineering students in graduate level the expertise necessary to understand and use computational methods for the approximate/numerical solution of linear algebra problems that arise in many different fields of science like electrical networks, solid mechanics, signal analysis and optimisation. The emphasis is on methods for linear algebra problems such as solutions of linear systems, least squares problems and eigenvalue-eigenvector problems, the effect of roundoff on algorithms and the citeria for choosing the best algorithm for the mathematical structure of the problem under consideration.
Course Learning Outcomes The students who succeeded in this course;
  • After successful completion of the course the student will be able to: 1-choose an efficient method to solve (large) linear systems, eigenvalue problems and least squares problems coming from a certain application field, 2-implement the methods and/or algorithms as computer code and use them to solve applied problems, 3-discuss the numerical methods and/or algorithms with respect to stability, applicability, reliability, conditioning, accuracy, computational complexity and efficiency.
Course Content Floating point computations, vector and matrix norms, direct methods for the solution of linear systems, least squares problems, eigenvalue problems, singular value decomposition, iterative methods for linear systems.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Introduction to numerical computations. Vector and matrix norms Read related sections in references
2 Condition numbers and conditioning, Stability, Propogation of roundoff errors Read related sections in references
3 Direct methods for linear systems, Gaussian elimination, Pivoting, Stability. LU and Cholesky decompositions Read related sections in references
4 LU and Cholesky decompositions (cont.) Operation counts, Error analysis, Perturbation theory, Special linear systems Read related sections in references
5 Least Squares. Orthogonal matrices, Normal equations, QR factorization Read related sections in references
6 Gram-Schmidt orthogonalization, Householder triangularization, Least Squares problems Read related sections in references
7 Eigenproblem. Eigenvalues and eigenvectors, Gersgorin’s circle theorem, Iterative methods for eigenvalue problems Read related sections in references
8 Power, Inverse Power and Shifted Power methods, Rayleigh quotients, Similarity transformations, Reduction to Hessenberg and tridiagonal forms Read related sections in references
9 QR algorithm for eigenvalues and eigenvectors, Other eigenvalue algorithms. Singular Value Decomposition Read related sections in references
10 SVD(cont.) and connection with Lesat Squares problem, Computing the SVD using the QR algorithm Read related sections in references
11 Iterative Methods for Linear Systems. Basic iterative methods, Jacobi, and Gauss-Seidel methods Read related sections in references
12 Richardson and SOR methods, Convergence analysis of the iterative methods Read related sections in references
13 Krylov subspace Methods, Preconditioning and preconditioners Read related sections in references
14 General Review -
15 General Review -
16 Final exam -

Sources

Course Book 1. L.N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997.
2. J.W.Demmel, Applied Numerical Linear Algebra, SIAM, 1997
Other Sources 3. G.H. Golub and C.F. van Loan. Matrix Computations, John Hopkin’s University Press, 3rd edition, 1996.
4. A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM, 1997.
5. C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000.
6. O. Axelsson, Iterative Solution Methods, Cambridge University Press, 1996.
7. D.S. Watkins, Fundamentals on Matrix Computations, John Wiley and Sons, 1991.
8. K.E.Atkinson, An Introduction to Numericall Analysis, John Wiley and Sons, 1999.

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics 5 10
Homework Assignments 7 9
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 46
Final Exam/Final Jury 1 35
Toplam 15 100
Percentage of Semester Work 65
Percentage of Final Work 35
Total 100

Course Category

Core Courses X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 An ability to access, analyze and evaluate the knowledge needed for the solution of advanced chemical engineering and applied chemistry problems.
2 An ability to self-renewal by following scientific and technological developments within the philosophy of lifelong learning.
3 An understanding of social, environmental, and the global impacts of the practices and innovations brought by chemistry and chemical engineering.
4 An ability to perform original research and development activities and to convert the achieved results to publications, patents and technology.
5 An ability to apply advanced mathematics, science and engineering knowledge to advanced engineering problems.
6 An ability to design and conduct scientific and technological experiments in lab- and pilot-scale, and to analyze and interpret their results.
7 Skills in design of a system, part of a system or a process with desired properties and to implement industry.
8 Ability to perform independent research.
9 Ability to work in a multi-disciplinary environment and to work as a part of a team.
10 An understanding of the professional and occupational responsibilities.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
Homework Assignments 7 3 21
Quizzes/Studio Critics 5 1 5
Prepration of Midterm Exams/Midterm Jury 2 8 16
Prepration of Final Exams/Final Jury 1 10 10
Total Workload 132