Numerical Linear Algebra (MAE685): Διαφορά μεταξύ των αναθεωρήσεων
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| Γραμμή 56: | Γραμμή 56: | ||
! 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 | ||
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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. | ||
* | * 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. 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. | ||
Αναθεώρηση της 23:56, 28 Σεπτεμβρίου 2022
Undergraduate Courses Outlines - Department of Mathematics
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. 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 |
| ||||||||||
| 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.