Stable Discretization
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms — Stable Discretization
From the book
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms. In the chapter mind map this icon labels Stable Discretization. The discussion below is excerpted and lightly edited from § Stable Discretization in Mathematics for AI and Machine Learning.
To implement continuous-time dynamics on digital computers, we must discretize the equations. Given a time step $\Delta > 0$, we seek a discrete-time system:
that approximates the continuous dynamics. Different discretization methods yield different $\bar{A}$ and $\bar{B}$.
What this drawing shows
What you see. Left-half-plane $\mathrm{Re}<0$ region brightens while the Euler stability disk fades, contrasting stability-preserving vs Euler maps.
In the mind map. Chapter 20 — Stable Discretization. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 20: ODE, SDE, and Continuous Limits of Algorithms — see the mind-map node Stable Discretization.
