Orthogonality and the Machine's Blind Spot
Автор: jetbundle
Загружено: 2026-01-19
Просмотров: 59
Описание:
The reason why Finite Element Analysis is called a projection method is made clear. We prove that the machine, restricted by its grid, automatically finds the optimal compromise that minimizes the energy error. The “dumb” arithmetic units doing multiply/adds at the bit level have no concept of “best fit” or “projection.” But because they perform virtual work on a sparse graph built on the weak form, the state of the solution is guaranteed by Céa’s lemma to be the optimal energy projection of infinite reality onto their bit world.
00:00 Recapitulation
08:00 Galerkin Orthogonality
17:32 Céa’s Lemma
27:45 Interpretation
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