General
School
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School of Science
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Academic Unit
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Department of Mathematics
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Level of Studies
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Graduate
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Course Code
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AA3A
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Semester
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1
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Course Title
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Numerical Linear Algebra I
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Independent Teaching Activities
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Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
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Course Type
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Special Background
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Prerequisite Courses
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-
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Language of Instruction and Examinations
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Greek
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Is the Course Offered to Erasmus Students
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Yes (in English)
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Course Website (URL)
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-
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Learning Outcomes
Learning outcomes
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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.
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General Competences
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- 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
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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
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In the class
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Use of Information and Communications Technology
|
-
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Teaching Methods
|
Activity
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Semester Workload
|
Lectures
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39
|
Study and analysis of bibliography
|
78
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Preparation of assignments and interactive teaching
|
70.5
|
Course total
|
187.5
|
|
Student Performance Evaluation
|
Written examination - Oral Examination.
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Attached Bibliography
- Numerical Linear Algebra, Dougalis V., Noutsos D., Hadjidimos A., University of Ioannina Press
- Personal Transparencies.