PhD in Mathematics

Kernel-based approximation and quasi-Monte Carlo integration

Academic year 2024/2025

Sommario del corso

• Program
• Notes
• Teaching tools
• Course card

Program

The teaching aims to provide knowledge on some topics of kernel-based approximation and quasi-Monte Carlo integration methods. Kernel methods play an important role in many different areas of mathematics, science, and engineering. They are of particular interest in the field of multivariate scattered data interpolation and solution of partial differential equations using radial basis functions (RBFs). The goal is, on one hand, to introduce theory and, on the other, to show application of related numerical methods. Quasi-Monte Carlo (qMC) and Monte Carlo (MC) methods for integration are a decisive step in overcoming the so-called “curse of dimensionality” when you deal with the approximation of integral in high-dimensions. Nevertheless, the advantages of the first, compared to the second, are many. MC method is a numerical method based on random sampling, whereas in qMC method these samples are replaced by well-chosen deterministic points. The aim is to select these points in order that the deterministic error is smaller than the probabilistic error bound of MC method.

Notes

• Teaching material
• Exams and finals
• Class schedule
• Go to Moodle
• Register for the course
• Enrolled students
• Invia email agli studenti registrati
• Export table