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Numerical Linear Algebra II (AA4): Διαφορά μεταξύ των αναθεωρήσεων

Numerical Linear Algebra II (AA4): Διαφορά μεταξύ των αναθεωρήσεων

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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Αριθμητική Γραμμική Άλγεβρα II (ΑΑ4)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
Γραμμή 49: Γραμμή 51:
! Learning outcomes
! Learning outcomes
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|
ΧΧΧ
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.
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|-
! General Competences
! General Competences
|
|
ΧΧΧ
* 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 ===
=== Syllabus ===


ΧΧΧ
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 ===
=== Teaching and Learning Methods - Evaluation ===
Γραμμή 66: Γραμμή 77:
! Delivery
! Delivery
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ΧΧΧ
In the classroom
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|-
! Use of Information and Communications Technology
! Use of Information and Communications Technology
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| -
ΧΧΧ
|-
|-
! Teaching Methods
! Teaching Methods
Γραμμή 81: Γραμμή 91:
| 39
| 39
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| ΧΧΧ
| Study and analysis of bibliography
| 000
| 78
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|-
| ΧΧΧ
| Exercises - Homework
| 000
| 70.5
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|-
| Course total  
| Course total  
Γραμμή 93: Γραμμή 103:
! Student Performance Evaluation
! Student Performance Evaluation
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ΧΧΧ
Written examination - Oral Examination
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Τελευταία αναθεώρηση της 05:15, 16 Ιουνίου 2023

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.
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