Numerical Linear Algebra (MAE685)

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.