Approximation Theory (AA2): Διαφορά μεταξύ των αναθεωρήσεων

Αναθεώρηση της 10:15, 10 Νοεμβρίου 2022

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	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

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.

Delivery

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Use of Information and Communications Technology

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Teaching Methods

Student Performance Evaluation

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 === Syllabus ===
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+* 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 ===