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The translation from continuous to discrete is not automatic. There is a missing verification in the linked analysis. The mapping must be verified for stability
by measurablefunc 6mo ago
The translation from continuous to discrete is not automatic. There is a missing verification in the linked analysis. The mapping must be verified for stability for the proper class of initial/boundary conditions. Increasing the resolution from 64 bit floats to 128 bit floats doesn't automatically give you a stable discretized optimizer from a continuous formulation.
- phyalow 6mo agoOr you can just try stuff and see if it works
- measurablefunc 6mo agoPoint still stands, translation from continuous to discrete is not as simple as people think.
- phreeza 6mo agoNumerical issues totally exist but the reason has nothing to do with the fact that Cauchy sequences don't exist on a computer imo.
- measurablefunc 6mo agoThe abstract formulation is different from the concrete implementation. It is precisely b/c the abstractions do not exist on computers that the abstract analysis does not automatically transfer the necessary analytical properties to the digital implementation. Cauchy sequences & Dedekind cuts are abstract & do not exist on digital computers.