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13D081TA - Approximation Theory

Course specification
Course title Approximation Theory
Acronym 13D081TA
Study programme Electrical Engineering and Computing
Module
Type of study doctoral studies
Lecturer (for classes)
Lecturer/Associate (for practice)
    Lecturer/Associate (for OTC)
      ESPB 9.0 Status elective
      Condition Knowledge of classical mathematical analysis, notion of basic terms and methods of numerical analysis.
      The goal Introducing students to methods of approximation theory and ways of choosing appropriate methods depending on nature of problems, guiding students to independently conduct research and follow contemporary topics in this field.
      The outcome Students are capable to apply methods of approximation theory in electrotechnics and to conduct independent research and follow contemporary topics in this field.
      Contents
      Contents of lectures Constructive elements and approaches in approximation theory. Orthogonal polynomials and weighted polynomial approximation. Fundamental three-term recurrence relation. Chebyshev system of functions and interpolation. Quadrature processes. Numerical construction of quadratures. Golub-Welsch algorithm. Applications in electrotechnics, signal processing and computer science.
      Contents of exercises Through examples, assignments and analysis of scientific papers, a student learns how to apply the basic concepts he has learned in the theoretical part. Likewise, the student is referred to the literature monitoring for writing seminar papers and scientific papers.
      Literature
      1. Mastroianni, G., Milovanović, G.V., Interpolation Processes – Basic Theory and Applications, Springer, 2008. (Original title)
      2. Gautschi, W., Orthogonal Polynomials: Computation and Approximation, Clarendon Press, Oxford, 2004. (Original title)
      3. DeVore, R.A., Lorentz, G.G., Constructive Approximation, Springer, 1993. (Original title)
      Number of hours per week during the semester/trimester/year
      Lectures Exercises OTC Study and Research Other classes
      6
      Methods of teaching Traditional lectures with use of computers and modern mathematical software tools. Mentoring work with students, consultations.
      Knowledge score (maximum points 100)
      Pre obligations Points Final exam Points
      Activites during lectures Test paper 70
      Practical lessons Oral examination
      Projects
      Colloquia
      Seminars 30