Numerical Linear Algebra II (AA4)

General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	AA4
Semester	1
Course Title	Numerical Linear Algebra II
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 Greek)
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: know and understand the theory of methods for computation of the eigenvalues and singular values, know from applications, the necessity of this theory, 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 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

Numerical methods for the computation of Eigenvalues and Eigenvectors: Power Method, QR Method, Stable algorithms (Howsholder Reflections, Givens Rotations). Singular Values: Singular Value Decomposition. Krylov subspace Methods for the solution of Large Scale Linear Systems: Preconditioned Conjugate Gradient Method. Generalized Minimal Residual Method (GMRES): Theory of Orthogonalization of Krylov Subspaces, Arnoldi and Lanczos Algorithms. Applications of Iterative Methods to boundary value problems and to Signal and Image Processing.

Teaching and Learning Methods - Evaluation

Delivery

In the classroom

Use of Information and Communications Technology

-

Teaching Methods

Activity	Semester Workload
Lectures	39
Study and analysis of bibliography	78
Exercises - Homework	70.5
Course total	187.5

Student Performance Evaluation

Written examination - Oral Examination

Attached Bibliography

“Αριθμητική Γραμμική Άλγεβρα”, Β. Δουγαλής, Δ. Νούτσος, Α. Χατζηδήμος, Τυπογραφείο Πανεπιστημίου Ιωαννίνων.
“Matrix Computations”, G. H. Golub, C. F. Van Loan, The John Hopkings University Press, Baltimore and London, 1996.