Approximation Theory (AA2)

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• Graduate Courses Outlines
• Department of Mathematics

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.