Computer-assisted proofs in nonlinear analysis

J. B. van den Berg, M. Breden, O. Hénot, J.-P. Lessard, J. D. Mireles James.
Lessons, applications and exercises, with IntervalArithmetic.jl and RadiiPolynomial.jl.

source · proof packages

0 · Getting started

• Installation
• Cheatsheets

1 · Finite-dimensional problems

• Lesson: Finite-dimensional problems
• Exercise 1: Operator norms
• Exercise 2: Rigorous computation of an eigenpair
• Exercise 3: Rigorous inverse of a matrix
• Exercise 4: Rigorous control of the entire spectrum
• Exercise 5: Toward rigorous continuation

2 · Algebraic equations

• Lesson: Algebraic equations
• Exercise 1: Sequence space properties
• Exercise 2: Inverse function for infinite sequences
• Exercise 3: Radius of convergence
• Exercise 4: Roots

3 · Taylor integration

• Lesson: Taylor integration

4 · Periodic orbits

• Lesson: Periodic orbits

5 · Invariant manifolds of equilibria

• Lesson: Parameterization method
• Application: Lorenz system
• Exercise 1: Stable and unstable manifolds
• Exercise 2: 2D manifold