Euler vs Bilinear Discretization
From the book
Chapter 20: ODE, SDE, and Continuous Limits of Algorithms. In the chapter mind map this icon labels Euler and Bilinear (Tustin) Discretization. The discussion below is excerpted and lightly edited from § Euler and Bilinear (Tustin) Discretization in Mathematics for AI and Machine Learning.
- Second-order accurate
- Maps stable continuous systems to stable discrete systems (stability-preserving)
- Maps imaginary axis to unit circle exactly
- Requires matrix inverse (one-time computation)
What this drawing shows
What you see. Red forward-Euler points fade as the green bilinear (Tustin) discretization builds point by point along the reference decay.
In the mind map. Chapter 20 — Euler and Bilinear (Tustin) 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 Euler and Bilinear (Tustin) Discretization.
