◆ core20 mindraft
Conditioning versus stability
Two different questions that get confused constantly: is the problem sensitive, or is my algorithm sloppy? One you can fix, the other you cannot.
assumes you already have
Planned outline
- The condition number of a problem, and why it is a property of the question rather than the method.
- Backward stability: a stable algorithm gives the exact answer to a nearby question.
- Worked case: solving a nearly singular 2x2 system, where no algorithm can rescue you.
- Worked case: the quadratic formula, where the naive root is unstable and the rearranged one is not.
- Rule of thumb: relative error ≤ condition number x machine epsilon, for a backward-stable algorithm.
Interactives planned
Each numbered point above gets at least one thing you can manipulate, not a figure. See
AGENTS.md for the widget vocabulary and the rule that every lesson ships at least one
graded interaction and one recall card.