Syllabus
Interval linear algebra:
- interval linear systems of equations and inequalities
(description, complexity, methods),
- regularity of interval matrices,
- eigenvalues of interval matrices.
(Interval) nonlinear systems of equations.
Interval linear programming.
Global optimization using interval analysis.
Annotation
Interval computations provide rigorous bounds for numerical output. For this reasons, it is used in validated computing with floating-point arithmetic, e.g. in computer-aided proofs of famous math conjectures (The Kepler
Conjecture, The double bubble problem etc.). It gives verified solutions in solving (non)linear systems of equations and in global optimization.
Remark: The course can be tought once in two years.