Numerical Linear Algebra I (ΑΑ3)

Graduate Courses Outlines - Department of Mathematics

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	AA3A
Semester	1
Course Title	Numerical Linear Algebra I
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
Is the Course Offered to Erasmus Students	Yes (in English)
Course Website (URL)	See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

After successful end of this course, students will be able to: know and understand the Perron-Frobenius Theory, know the differences of Perron-Frobenius Theory as applied to different classes of matrices (irreducible, cyclic, primitive and reducible), know the efficiency of the Perron-Frobenius Theory in applications, know and understand the theory of Krylov subspace methods, know error analysis, know the preconditioned techniques and the necessity of preconditioning, implement the above methods with programs on a computer.

General Competences

Search for, analysis and synthesis of data and information, with the use of the necessary technology Adapting to new situations Criticism and self-criticism Production of free, creative and inductive thinking

Syllabus

Perron-Frobenius Theory of Nonnegative Matrices: Irreducible Matrices, Cyclic and Primitive Matrices, Reducible Matrices, Extension of the Perron-Frobenius Theory, M-matrices, Applications of the Perron-Frobenius Theory. Minimization methods for the Solution of Linear Systems: Conjugate Gradient Method, Convergence Theory, Error Analysis, Preconditioning Techniques, Preconditioned Conjugate Gradient Methods, Applications.

Teaching and Learning Methods - Evaluation

Delivery	In the class
Use of Information and Communications Technology	-
Teaching Methods	Activity Semester Workload Lectures 39 Study and analysis of bibliography 78 Preparation of assignments and interactive teaching 70.5 Course total 187.5
Student Performance Evaluation	Written examination - Oral Examination.

Attached Bibliography

• Theodor J. Rivlin: An Introduction to the Approximation of Functions. Dover Publications Inc. New York, 1969.