Lesson 7.2 · 23 of 25 lessons
Iterative computation
See how conditioning magnifies input error and how repeated computation converges toward one direction.
Open the interactive animation01 · Story
What to verify in this scene
Follow the explanations and operations, then identify the mathematical evidence that remains in the final scene.
- 01
Each application of A halves the y component while preserving the x component
- 02
Apply the same A again and watch which direction v approaches
- 03
v moves closer to the x-axis
Iterative methods exploit this dominant direction
02 · Notebook
The runnable notebook
This source creates the mathematical objects and controls the order of operations and animation. Read it here, then play the same scene yourself.
2d
zoom 4/5
grid off
relative-grid on
coordinates on
1 0 #A
0 1/2
2, 2 #v@
// Each application of {{A}} halves the y component while preserving the x component
checkpoint Iterative computation
A
// Apply the same {{A}} again and watch which direction {{v}} approaches
A
A
// {{v}} moves closer to the x-axis\nIterative methods exploit this **dominant direction**
focus v03 · Unit 7
Lessons in this unit
Matrix computation & stability — See how conditioning magnifies input error and how repeated computation converges toward one direction.