The student has already studied, in the basic course of numerical analysis, some problems and the corresponding algorithms for solving countinuum problems in a discrete way. The course aims to deep more other fields in which it is fundamental, having at disposal, efficient and stable numerical methods for the solution of problems coming from real applications, i.e. not only in the univariate setting.
The course is carried out in 40 hours of lecture / tutorial. A few hours of exercises will be conducted as a laboratory for which it will be necessary the use of programming languages studied in previous courses, in particularl Matlab or Octave. During the hours of lab, students will be asked to do the implementations of some of the numerical methods presented during lectures and to solve simple problems in order to better appreciate the issues addressed in the course.
The theme will focus mainly on Radial Basis Functions or RBF.
- Radial Basis Function (RBF).
Generality, positive definite and conditionally positive definite functions. Interpolation and approximation with RBF (scattered data, least squares). Solution of ill-conditioned systems. Applications to differential equations (pseudo-spectral methods).
In order to better understanding the topics, we kindly invite the students to participate actively at lecture and tutorials/lab.
- practical test (implementation in Matlab/Octave)
- (eventually) an interview.
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