Math Courses

PILLAR course: Numerical Analysis

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Ex-INPS building (GSSI)

Ex-INPS building

GSSI
Description

Lecturers

Nicola Guglielmi nicola.guglielmi@gssi.it                                              

Francesco Paolo Maiale francescopaolo.maiale@gssi.it

Marco Sutti marco.sutti@gssi.it


Timetable and workload
Lectures: 60 hours
Calendar: available at this link

Course description and outcomes
This course is an introduction to some topics of modern numerical analysis. The primary objective of the course is to develop graduate-level understanding of computational mathematics and skills to solve a range real-world mathematical problems on a computer by implementing advanced numerical algorithms using a scientific computing language (such as MATLAB or Python). The main topics covered by the course consist of numerical integration of differential equations, and numerical methods for continuous optimization. Special topics will include delay differential equations and eigenvalue optimization with applications.

 

Course requirements
Calculus, linear algebra and basic numerical analysis. Previous programming experience in any language may help. Further details on recommended previous knowledge in numerical analysis can be found in the course programme document, which is uploaded in the Materials section.

Course content
The course will cover the following topics (further details can be found in the course program document uploaded in the Materials section):

  1. Numerical integration of differential equations - 1.1 Quadrature; 1.2 One step methods for ODEs; 1.3 Adaptation to DDEs
  2. Numerical optimization - 2.1 Gradient methods; 2.2 Constrained optimization
  3. Matrix nearness problems and eigenvalue optimization - 3.1 Eigenvalue optimization

References

  • R. Fletcher, Practical methods of optimization. Second edition. Wiley-Interscience [John Wiley & Sons], New York, 2001. xiv+436 pp.
  • W. Gautschi, Numerical analysis. An introduction. Birkh¨auser Boston, Inc., Boston, MA, 1997.
  • N. Guglielmi and C. Lubich: Matrix nearness problems and eigenvalue optimization, https://arxiv.org/abs/2503.14750
  • E. Hairer, S. Nørsett and G. Wanner, Solving ordinary differential equations. I. Nonstiff problems. Second edition. Springer Series in Computational Mathematics, 8. Springer-Verlag, Berlin, 1993.
  • J. Nocedal and S.J. Wright, Numerical Optimization. Second edition, Springer, New York, 2006.
  • J. Stoer and R. Bulirsch, Introduction to numerical analysis. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. Third edition. Texts in Applied Mathematics, 12. Springer-Verlag, New York, 2002.

 

Examination and grading
Written exam and practical (computational) assessment at the end of the course.

 

Anonymous survey link: here. 

Course Program.pdf