Approximation Theory (AA2): Διαφορά μεταξύ των αναθεωρήσεων
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=== General === | === General === | ||
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|- | |- | ||
! Course Code | ! Course Code | ||
| | | AA2 | ||
|- | |- | ||
! Semester | ! Semester | ||
| | | 1 | ||
|- | |- | ||
! Course Title | ! Course Title | ||
| | | Approximation Theory | ||
|- | |- | ||
! Independent Teaching Activities | ! Independent Teaching Activities | ||
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|- | |- | ||
! Course Type | ! Course Type | ||
| | | Special Background | ||
|- | |- | ||
! Prerequisite Courses | ! Prerequisite Courses | ||
Γραμμή 34: | Γραμμή 36: | ||
! Language of Instruction and Examinations | ! Language of Instruction and Examinations | ||
| | | | ||
Greek | |||
|- | |- | ||
! Is the Course Offered to Erasmus Students | ! Is the Course Offered to Erasmus Students | ||
| Yes | | | ||
Yes (in English) | |||
|- | |- | ||
! Course Website (URL) | ! Course Website (URL) | ||
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! Learning outcomes | ! Learning outcomes | ||
| | | | ||
After successful end of this course, students will be able to: | |||
* know the basic items of approximation from a linear space to a subspace, | |||
* know the differences (advantages and disadvantages) of different kinds of approximations, | |||
* know the basic numerical methods for the polynomial approximation, | |||
* implement the algorithms of such methods on a computer. | |||
|- | |- | ||
! General Competences | ! 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 === | === Syllabus === | ||
* General Theory of existence and uniqueness of approximation. | |||
* Uniform Approximation: Weierstrass, Bernstein, Jackson theorems, approximation of continuous functions, approximation of discrete functions, Remez algorithm. | |||
* Least Squares Polynomial Approximation: Systems of Normal Equations, Orthogonal Polynomials, approximation of continuous functions, approximation of discrete functions, connection with Uniform approximation. | |||
* First Power Polynomial Approximation: Characterization, approximation of continuous functions, approximation of discrete functions,. | |||
* Rational Approximation: Characterization, connection with Uniform approximation, Remez algorithm. | |||
* Rational Interpolation. | |||
=== Teaching and Learning Methods - Evaluation === | === Teaching and Learning Methods - Evaluation === | ||
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! Delivery | ! Delivery | ||
| | | | ||
In the classroom | |||
|- | |- | ||
! Use of Information and Communications Technology | ! Use of Information and Communications Technology | ||
| | | - | ||
|- | |- | ||
! Teaching Methods | ! Teaching Methods | ||
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| 39 | | 39 | ||
|- | |- | ||
| | | Working Independently | ||
| | | 78 | ||
|- | |- | ||
| | | Exercise - Homework | ||
| | | 70.5 | ||
|- | |- | ||
| Course total | | Course total | ||
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! Student Performance Evaluation | ! Student Performance Evaluation | ||
| | | | ||
Written examination | |||
|} | |} | ||
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Τελευταία αναθεώρηση της 05:14, 16 Ιουνίου 2023
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General
School | School of Science |
---|---|
Academic Unit | Department of Mathematics |
Level of Studies | Graduate |
Course Code | AA2 |
Semester | 1 |
Course Title | Approximation Theory |
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 English) |
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:
|
---|---|
General Competences |
|
Syllabus
- General Theory of existence and uniqueness of approximation.
- Uniform Approximation: Weierstrass, Bernstein, Jackson theorems, approximation of continuous functions, approximation of discrete functions, Remez algorithm.
- Least Squares Polynomial Approximation: Systems of Normal Equations, Orthogonal Polynomials, approximation of continuous functions, approximation of discrete functions, connection with Uniform approximation.
- First Power Polynomial Approximation: Characterization, approximation of continuous functions, approximation of discrete functions,.
- Rational Approximation: Characterization, connection with Uniform approximation, Remez algorithm.
- Rational Interpolation.
Teaching and Learning Methods - Evaluation
Delivery |
In the classroom | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Use of Information and Communications Technology | - | ||||||||||
Teaching Methods |
| ||||||||||
Student Performance Evaluation |
Written examination |
Attached Bibliography
- Theodor J. Rivlin: An Introduction to the Approximation of Functions. Dover Publications Inc. New York, 1969.