# Numerical Linear Algebra (MAE685)

### General

School School of Science Department of Mathematics Undergraduate ΜΑΕ685 6 Numerical Linear Algebra Lectures (Weekly Teaching Hours: 3, Credits: 6) Special Background - Greek Yes (in English) See eCourse, the Learning Management System maintained by the University of Ioannina.

### Learning Outcomes

Learning outcomes Upon successful completion of this course, students will be able to: describe and apply numerical methods from a variety of linear algebra problems. recognize the limitations of finite precision arithmetic in calculations and explain the importance of the stability of numerical algorithms. evaluate numerical methods for their accuracy, efficiency, and applicability. implement in Octave or Python numerical algorithms and apply appropriate criteria to terminate an iterative algorithm. Search for, analysis and synthesis of data and information, with the use of the necessary technology. Adapting to new situations. Working independently. Production of free, creative, and inductive thinking. Promotion of analytical and synthetic thinking. Decision-making.

### Syllabus

• Introduction to matrix theory. Singular Value Decomposition (SVD). Matrix condition number and conditioning of linear systems.
• The linear least squares problem, QR method, Householder transformations.
• Direct methods (LU Factorization, Cholesky Factorization).
• Iterative methods: Jacobi, Gauss-Seidel, SOR method, steepest descent method, conjugate gradient method.
• Computation of eigenvalues ​​and eigenvectors.
• Applications (PageRank Google search algorithm, image processing, etc.)

### Teaching and Learning Methods - Evaluation

Delivery

Face-to-face

Use of Information and Communications Technology
• Use of a tablet device to deliver teaching. Lecture materials in pdf-format are made available to students, for later review, on Moodle e-learning platform.
• Provision of study materials in Moodle e-learning platform.
• Provision of model solutions for some exercises in podcast format.
• Communication with students through e-mails, Moodle platform and Microsoft Teams.
• IT sessions (Python or Octave) for the implementation of the numerical algorithms.
Teaching Methods
Lectures 39
Study and analysis of bibliography 76
Directed study of exercises 5
Exercises-Homeworks 30
Course total 150
Student Performance Evaluation
• Computer-based exercises with oral examination (Weighting 30%, addressing learning outcomes 2-4)
• Written examination (Weighting 100%, addressing learning outcomes 1-3)

### 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.