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Approximation Theory (AA2): Διαφορά μεταξύ των αναθεωρήσεων

Approximation Theory (AA2): Διαφορά μεταξύ των αναθεωρήσεων

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[[Graduate Courses Outlines]] - [https://math.uoi.gr  Department of Mathematics]
* [[Θεωρία Προσεγγίσεως (ΑΑ2)|Ελληνική Έκδοση]]
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=== General ===
=== General ===
Γραμμή 50: Γραμμή 52:
! Learning outcomes
! Learning outcomes
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|
ΧΧΧ
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.
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|-
! General Competences
! General Competences
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|
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
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=== Syllabus ===
=== Syllabus ===


ΧΧΧ
* 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 ===
Γραμμή 67: Γραμμή 81:
! 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 82: Γραμμή 95:
| 39
| 39
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|-
| ΧΧΧ
| Working Independently
| 000
| 78
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| ΧΧΧ
| Exercise - Homework
| 000
| 70.5
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| Course total  
| Course total  
Γραμμή 94: Γραμμή 107:
! Student Performance Evaluation
! Student Performance Evaluation
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ΧΧΧ
Written examination
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Γραμμή 100: Γραμμή 113:


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Τελευταία αναθεώρηση της 05:14, 16 Ιουνίου 2023

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:

  • 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
  • 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

  • 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
Activity Semester Workload
Lectures 39
Working Independently 78
Exercise - Homework 70.5
Course total 187.5
Student Performance Evaluation

Written examination

Attached Bibliography

  • Theodor J. Rivlin: An Introduction to the Approximation of Functions. Dover Publications Inc. New York, 1969.
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