ECTS - Numerical Linear Algebra
Numerical Linear Algebra (MDES621) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Numerical Linear Algebra | MDES621 | Area Elective | 3 | 0 | 0 | 3 | 5 |
| Pre-requisite Course(s) |
|---|
| N/A |
| Course Language | English |
|---|---|
| Course Type | Core Course |
| Course Level | Ph.D. |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture. |
| Course Lecturer(s) |
|
| 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;
|
| 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 | Ability to carry out advanced research activities, both individual and as a member of a team | X | ||||
| 2 | Ability to evaluate research topics and comment with scientific reasoning | X | ||||
| 3 | Ability to initiate and create new methodologies, implement them on novel research areas and topics | X | ||||
| 4 | Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions | X | ||||
| 5 | Ability to apply scientific philosophy on analysis, modelling and design of engineering systems | X | ||||
| 6 | Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level | X | ||||
| 7 | Contribute scientific and technological advancements on engineering domain of his/her interest area | X | ||||
| 8 | Contribute industrial and scientific advancements to improve the society through research activities | X | ||||
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 | ||