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 | Elective Courses |
| 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 | Is independently able to build a problem in the area of study, solve the problem by developing solution techniques and assess the solutions. | X | ||||
| 2 | Is capable of creating a groundwork in the fundamental branches of mathematics as well as in his/her research area | X | ||||
| 3 | follows the latest national and international literature in Mathematics and in his/her area of research; and uses them in his/her related studies | X | ||||
| 4 | observes and adopts the scientific ethical values in his/her professional and social life | X | ||||
| 5 | presents in Turkish and English in academic/scientific events the results of his/her research or the latest studies and findings on a special topic and participates in discussions | X | ||||
| 6 | Develops skills to work independently or as a member of a team | X | ||||
| 7 | Develops competences in the areas of creative and critical thinking, problem solving and producing original studies. Follows recent scientific studies, is capable of making an analysis, synthesis and assessment of the knowledge acquired | X | ||||
| 8 | Is open to lifelong improvement of his/her acquired knowledge, skills and competences. | X | ||||
| 9 | Is able to apply the acquired knowledge and problem-solving skills to interdisciplinary studies, proposes different solution methods to problems in terms of mathematical models and from a mathematical point of view | X | ||||
| 10 | Uses the mathematical based softwares, informatics and communication technologies for scientific purposes | 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 | ||