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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5012 NUMERICAL ANALYSIS FOR MATRICES AND SYSTEMS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

Offered to

Mathematics (English) Mathematics (English)

Course Objective

This course will cover the development and analysis of numerical linear algorithms used in the solution of linear equations, eigenvalue problems, and linear least-square problems

Learning Outcomes of the Course Unit

1   will be able to understand the basic theory and techniques in numerical linear algebra 2   will be able to understand the algorithms for matrix factorizations 3   will be able to understand the algorithms for solving systems of linear equations (direct and iterative methods) 4   will be able to understand the algorithms for solving linear least squares problems 5   will be able to understand the algorithms for solving eigenvalue problems and singular value problems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Fundamentals Vector Space and Matrix, Norms Eigenvalues and Jordon Canonical Form Conditioning and Stability 2 Matrix Factorization Projectors QR Factorization and Gram-Schmidt Orthogonalization 3 Matrix Factorization Householder Triangularization LU Factorization and Cholesky Factorization 4 Systems of Equations Gaussian Elimination Pivoting 5 Systems of Equations Stability Analysis 6 Systems of Equations Iterative Methods Preconditioning 7 Midterm 8 Least Squares Problems Applications Overdetermined Least Squares Problems 9 Least Squares Problems Underdetermined Least Squares Problems 10 Eigenvalues Supplementary Knowledge of Eigenvalues Problem 11 Eigenvalues Reduction to Hessenberg or Tridiagonal Form 12 Eigenvalues Rayleigh Quotient, Inverse Iteration QR Algorithm 13 Computing the Singular Value Decomposition 14 Pseudoinverse. Perturbation theory

Recomended or Required Reading

Lloyd N. Trefethen and David Bau , Numerical Linear Algebra, SIAM, 1997 C. D. Meyer , Matrix Analysis and Applied Linear Algebra G. Golub and C. Van Loan, Matrix Computation, 3rd Ed., Johns Hopkins University Press, 1996. J.W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997. N.J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 1996.

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Homeworks

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.20 + ASG * 0.40 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.20 + ASG * 0.40 + RST * 0.40 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

sennur.somali@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 15 15 Preparation for final exam 1 25 25 Preparing assignments 10 5 50 Final 1 3 3 Midterm 1 3 3 TOTAL WORKLOAD (hours) 174

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 LO.1 5 5 5 4 4 5 4 4 3 3 4 LO.2 3 3 5 4 4 5 5 3 2 3 4 LO.3 3 3 5 4 4 5 5 3 2 4 4 LO.4 4 3 5 5 4 5 5 3 2 4 4 LO.5 4 4 5 5 4 5 5 3 2 4 4