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Numerical Linear Algebra I (ΑΑ3)

Numerical Linear Algebra I (ΑΑ3)

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General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Graduate
Course Code AA3
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:
  1. know and understand the Perron-Frobenius Theory,
  2. know the differences of Perron-Frobenius Theory as applied to different classes of matrices (irreducible, cyclic, primitive and reducible),
  3. know the efficiency of the Perron-Frobenius Theory in applications,
  4. know and understand the theory of Krylov subspace methods,
  5. know error analysis,
  6. know the preconditioned techniques and the necessity of preconditioning,
  7. implement the above methods with programs on a computer.
General Competences
  1. Search for, analysis and synthesis of data and information, with the use of the necessary technology
  2. Adapting to new situations
  3. Criticism and self-criticism
  4. 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.
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