# Numerical Analysis I (MATH521) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Numerical Analysis I MATH521 3 0 0 3 5
Pre-requisite Course(s)
Consent of the department
Course Language English N/A Ph.D. Face To Face Lecture, Discussion, Question and Answer, Problem Solving. Assoc. Prof. Dr. İnci Erhan This course is designed to give the expertise necessary to understand, construct and use computational methods for the numerical solution of linear algebra problems. The emphasis is on derivation and analysis of iterative methods for linear algebra problems as well as condition number, convergence, stability of algorithms and the criteria for choosing the best algorithm for the problem under consideration. The students who succeeded in this course; Understand the theoretical and practical aspects of the construction and implementation of the numerical methods Establish the advantages, disadvantages and limitations of the numerical methods and select the algorithms that converge to solutions in the most effective way Construct and apply iterative methods for the approximate solution of linear systems and eigenvalue-eigenvector problems, Estimate/determine the condition number of the linear system and condition the linear system whenever necessary Analyze the error and establish the conditions for convergence related to these methods Implement the methods and/or algorithms as computer code and use them to solve applied problems Discuss the numerical methods and/or algorithms with respect to stability, applicability, reliability, conditioning, accuracy, computational complexity and efficiency Matrix and vector norms, error analysis, solution of linear systems: Gaussian elimination and LU decomposition, condition number, stability analysis and computational complexity; least square problems: singular value decomposition, QR algorithm, stability analysis; matrix eigenvalue problems; iterative methods for solving linear systems: Jacobi, Ga

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Matrix and vector norms Atkinson- Sec. 7.3, Kress- Sec. 3.4
2 Error analysis: Absolute and relative error, floating point, round-off errors Atkinson-Sec.1.2-1.5
3 Solutions of linear systems: Gaussian elimination, pivoting and scaling Atkinson-Sec. 8.1,8.2 Kress-Sec. 2.2
4 LU decomposition Kress-Sec. 2.3,2.4
5 Condition numbers, stability, computational complexity Kress- Sec. 5.1
6 QR factorization: Householder transformation, Gram-Schmidt orthogonalization, Givens rotations Atkinson-Sec. 9.3, 9.5
7 Least square problems: Singular value decomposition Atkinson-Sec. 9.7 Kress-Sec. 5.2
8 Midterm Exam
9 Matrix eigenvalue problems: Estimates for eigenvalues, Jacobi method Atkinson-Sec. 9.1 Kress-Sec. 7.2,7.3
10 QR algorithm, Hessenberg Matrices Kress-Sec. 7.4,7.5
11 Schur factorization, Power method, Atkinson-Sec. 9.2, 9.6
12 Inverse Power method Atkinson-Sec. 9.2, 9.6
13 Iterative methods for linear systems: Jacobi Method Gauss-Seidel Method Kress-Sec. 4.1
14 Relaxation Methods Kress-Sec. 4.2
15 Conjugate gradient type methods Atkinson-Sec. 8.9
16 Final Exam

### Sources

Course Book 1. R. Kress, “Numerical Analysis: v. 181 (Graduate Texts in Mathematics)”, Kindle Edition, Springer, 1998. 2. K. E. Atkinson, “An Introduction to Numerical Analysis”, 2nd edition, John Wiley and Sons, 1989 3. G. H. Golub, C.F. Van Loan, “Matrix Computations”, North Oxford Academic, 1983. 4. R. L. Burden, R.J. Faires, “Numerical Analysis”, 9th edition, Brooks/ Cole, 2011.

### Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 7 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5

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 14 3 42
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 3 15
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 10 10
Prepration of Final Exams/Final Jury 1 10 10