Numerical Linear Algebra (MAE685): Διαφορά μεταξύ των αναθεωρήσεων
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[[ | * [[Αριθμητική Γραμμική Άλγεβρα (ΜΑΕ685)|Ελληνική Έκδοση]] | ||
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=== General === | === General === | ||
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! Course Code | ! Course Code | ||
| | | | ||
ΜΑΕ685 | |||
|- | |- | ||
! Semester | ! Semester | ||
| | | | ||
6 | |||
|- | |- | ||
! Course Title | ! Course Title | ||
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|- | |- | ||
! Course Website (URL) | ! Course Website (URL) | ||
| | | See [https://ecourse.uoi.gr/ eCourse], the Learning Management System maintained by the University of Ioannina. | ||
|} | |} | ||
=== Learning Outcomes === | === Learning Outcomes === | ||
{| class="wikitable" | {| class="wikitable" | ||
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! 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. | |||
* implement | |||
|- | |- | ||
! General Competences | ! General Competences | ||
| | | | ||
* Search for, analysis and synthesis of data and information, with the use of the necessary technology | * Search for, analysis and synthesis of data and information, with the use of the necessary technology. | ||
* Adapting to new situations | * Adapting to new situations. | ||
* | * Working independently. | ||
* Production of free, creative and inductive thinking | * Production of free, creative, and inductive thinking. | ||
* Promotion of analytical and synthetic thinking. | |||
* Decision-making. | |||
|} | |} | ||
=== Syllabus === | === Syllabus === | ||
Introduction to | |||
* 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 === | === Teaching and Learning Methods - Evaluation === | ||
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! Delivery | ! Delivery | ||
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Face-to-face | |||
|- | |- | ||
! Use of Information and Communications Technology | ! 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 | ! Teaching Methods | ||
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| 39 | | 39 | ||
|- | |- | ||
| Study and analysis of | | Study and analysis of bibliography | ||
| | | 76 | ||
|- | |||
| Directed study of exercises | |||
| 5 | |||
|- | |- | ||
| Exercises-Homeworks | | Exercises-Homeworks | ||
| | | 30 | ||
|- | |- | ||
| Course total | | Course total | ||
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! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
Written examination | * Computer-based exercises with oral examination (Weighting 30%, addressing learning outcomes 2-4) | ||
* Written examination (Weighting 100%, addressing learning outcomes 1-3) | |||
|} | |} | ||
=== Attached Bibliography === | === Attached Bibliography === | ||
<!-- In order to edit the bibliography, visit the webpage --> | |||
<!-- https://wiki.math.uoi.gr/index.php/%CE%A0%CF%81%CF%8C%CF%84%CF%85%CF%80%CE%BF:MAE685-Biblio --> | |||
See the official [https://service.eudoxus.gr/public/departments#20 Eudoxus site] or the [https://cloud.math.uoi.gr/index.php/s/62t8WPCwEXJK7oL local repository] of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus: | |||
{{MAE685-Biblio}} |
Τελευταία αναθεώρηση της 12:31, 15 Ιουνίου 2023
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General
School |
School of Science |
---|---|
Academic Unit |
Department of Mathematics |
Level of Studies |
Undergraduate |
Course Code |
ΜΑΕ685 |
Semester |
6 |
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 |
Upon successful completion of this course, students will be able to:
|
---|---|
General Competences |
|
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 |
| ||||||||||||
Teaching Methods |
| ||||||||||||
Student Performance Evaluation |
|
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.