Numerical Linear Algebra (MAE685)

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Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

ΜΑΕ685

Semester

5

Course Title

Numerical Linear Algebra

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

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:

  • understand the basic theory of matrices,
  • be aware of the taught methods to solve linear systems,
  • be aware of the taught methods for computing eigenvalues and eigenvectors,
  • choose the appropriate method by taking into account the stability and speed of the algorithm as well as the conditioning of the system.
  • implement the above methods with programs on the 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

Introduction to Matrix theory. Conditioning of Linear Systems, Stability of the methods. Direct methods: Gauss Elimination Method, LU Factorization, Cholesky Factorization. Iterative methods: Jacobi, Gauss-Seidel, Extrapolation technique, SOR method. Minimization methods for solving linear systems: steepest descent method, Conjugate Gradient method. The linear least squares problem: System of Canonical Equations, QR method. Computation of eigenvalues ​​and eigenvectors: Power Method, Inverse Power Method.

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 bibliografy 78
Exercises-Homeworks 33
Course total 150
Student Performance Evaluation

Written examination

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

  • “Αριθμητική Γραμμική Άλγεβρα”, Β. Δουγαλής, Δ. Νούτσος, & Α. Χατζηδήμος, Τυπογραφείο Πανεπιστημίου Ιωαννίνων.
  • “Numerical Linear Algebra”, L. Trefethen, & D. Bau, SIAM, 1997.
  • “Matrix Computations”, G. Golub, C. Van Loan, 3rd edition, Johns Hopkins Univ. Press 1996.
  • “Iterative Methods for Sparse Linear Systems”, Y. Saad, PWS Publishing, 1996.
  • “Linear Algebra and Learning from Data”, G. Strang, Wellesley-Cambridge Press, 2019.
  • “Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control”, S. Brunton, & J. Kutz, Cambridge: Cambridge University Press, 2019. doi:10.1017/9781108380690.