Numerical Linear Algebra (MAE685): Διαφορά μεταξύ των αναθεωρήσεων

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[[Undergraduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Αριθμητική Γραμμική Άλγεβρα (ΜΑΕ685)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
Γραμμή 18: Γραμμή 20:
! Course Code
! Course Code
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ΜΑΕ545
ΜΑΕ685
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|-
! Semester
! Semester
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|
5
6
|-
|-
! Course Title
! Course Title
Γραμμή 48: Γραμμή 50:
|-
|-
! 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"
Γραμμή 55: Γραμμή 58:
! Learning outcomes
! Learning outcomes
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After successful end of this course, students will be able to:
Upon successful completion of this course, students will be able to:
* understand the basic theory of matrices,
* describe and apply numerical methods from a variety of linear algebra problems.
* be aware of the taught methods to solve linear systems,
* recognize the limitations of finite precision arithmetic in calculations and explain the importance of the stability of numerical algorithms.
* be aware of the taught methods for computing eigenvalues and eigenvectors,
* evaluate numerical methods for their accuracy, efficiency, and applicability.
* choose the appropriate method by taking into account the stability and speed of the algorithm as well as  the conditioning of the system.
* implement in Octave or Python numerical algorithms and apply appropriate criteria to terminate an iterative algorithm.
* implement the above methods with programs on the computer.
|-
|-
! General Competences
! General Competences
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|
* 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.
* Criticism and self-criticism
* 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 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.
 
* 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 ===
{| class="wikitable"
{| class="wikitable"
Γραμμή 76: Γραμμή 88:
! Delivery
! Delivery
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In the class
Face-to-face
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|-
! 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
Γραμμή 90: Γραμμή 107:
| 39
| 39
|-
|-
| Study and analysis of bibliografy
| Study and analysis of bibliography
| 78
| 76
|-
| Directed study of exercises
| 5
|-
|-
| Exercises-Homeworks
| Exercises-Homeworks
| 33
| 30
|-
|-
| Course total  
| Course total  
Γραμμή 102: Γραμμή 122:
! Student Performance Evaluation
! Student Performance Evaluation
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|
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 ===
* “Numerical Linear Algebra”. Dougalis V., Noutsos D., Hadjidimos A., University of Ioannina.
 
<!-- 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

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:

  • 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.
General Competences
  • 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
Activity Semester Workload
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.