Information Package / Course Catalogue
Numerical Linear Algebra With Computer Applications
Course Code: MCS536
Course Type: Area Elective
Couse Group: Second Cycle (Master's Degree)
Education Language: English
Work Placement: N/A
Theory: 3
Prt.: 0
Credit: 3
Lab: 0
ECTS: 6
Objectives of the Course

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 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.

Name of Lecturer(s)
Learning Outcomes
1.At the end of the course the students are expected to: Choose an efficient method to solve (large) linear systems, eigenvalue problems and least squares problems coming from a certain application field,
2.Discuss the numerical methods and/or algorithms with respect to stability, applicability, reliability, conditioning, accuracy, computational complexity and efficiency.
3.Implement the methods and/or algorithms as computer code and use them to solve applied problems.
4.Establish the advantages, disadvantages and limitations of the numerical methods and select the algorithms that converge to solutions in the most effective way.
5.Analyze the error and establish the conditions for convergence related to these methods.
Recommended or Required Reading
1.L.N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997.
2.A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM, 1997.
3.C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, 2000
4.O. Axelsson, Iterative Solution Methods, Cambridge University Press, 1996.
5.J.W.Demmel, Applied Numerical Linear Algebra, SIAM, 1997
Weekly Detailed Course Contents
Week 1 - Theoretical
Introduction to numerical computations. Vector and matrix norms.
Week 2 - Theoretical
Condition numbers and conditioning, Stability, Propogation of roundoff errors.
Week 3 - Theoretical
Direct methods for linear systems, Gaussian elimination, Pivoting, Stability. LU and Cholesky decompositions.
Week 4 - Theoretical
LU and Cholesky decompositions (cont.) Operation counts, Error analysis, Perturbation theory, Special linear systems.
Week 5 - Theoretical
Least Squares. Orthogonal matrices, Normal equations, QR factorization.
Week 6 - Theoretical
Gram-Schmidt orthogonalization, Householder triangularization, Least Squares problems.
Week 7 - Theoretical
Eigenproblem. Eigenvalues and eigenvectors, Gersgorin’s circle theorem.
Week 8 - Theoretical
Iterative methods for eigenvalue problems ,Power, Inverse Power and Shifted Power methods.
Week 9 - Theoretical
Rayleigh quotients, Similarity transformations, Reduction to Hessenberg and tridiagonal forms
Week 10 - Theoretical
QR algorithm for eigenvalues and eigenvectors, Other eigenvalue algorithms. Singular Value Decomposition
Week 11 - Theoretical
SVD(cont.) and connection with Lesat Squares problem, Computing the SVD using the QR
Week 12 - Theoretical
Iterative Methods for Linear Systems. Basic iterative methods, Jacobi, and Gauss-Seidel methods
Week 13 - Theoretical
Computer Applications presentations-1
Week 14 - Theoretical
Computer Applications presentations-2
Assessment Methods and Criteria
Type of AssessmentCountPercent
Attending Lectures1%5
Project1%10
Midterm Examination1%15
Final Examination1%70
Workload Calculation
ActivitiesCountPreparationTimeTotal Work Load (hours)
Lecture - Theory143384
Project120323
Individual Work140114
Midterm Examination110313
Final Examination115318
TOTAL WORKLOAD (hours)152
Contribution of Learning Outcomes to Programme Outcomes
PÇ-1
PÇ-2
PÇ-3
PÇ-4
PÇ-5
PÇ-6
PÇ-7
PÇ-8
PÇ-9
OÇ-1
4
5
3
2
2
3
3
2
4
OÇ-2
2
3
2
2
2
2
2
2
5
OÇ-3
5
3
4
4
3
4
3
2
4
OÇ-4
3
3
3
4
2
3
3
3
4
OÇ-5
2
4
2
2
1
2
2
2
3
Adnan Menderes University - Information Package / Course Catalogue
2026