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> exact numerical solutions Isn't that an oxymoron? Numerical solutions always involve some sort of rounding errors because of limited floating-point precision
by majewsky 8y ago
> exact numerical solutions
Isn't that an oxymoron? Numerical solutions always involve some sort of rounding errors because of limited floating-point precision, so they cannot be exact.
- ChuckMcM 8y agoReminds me of the mathematician joke, "We know that one side of one house is painted brown." :-) You are correct in that most of these systems don't have a closed form solution that would yield an exact result, and they rely on either an interpolated value which is inexact depending on deviation or numerical solutions which typically iterate to the nearest point, that the system can represent in its limited 80 or 128 bit floating point system.
- zamadatix 8y agoA computer can be however exact you want it to be, that it supports floating point in hardware doesn't mean that is as accurate as it can get. It is far more apt to bring up most "interesting" solutions do not have an exact closed-form expression.
- ptero 8y agoOne can always build a counter-example, for example when candidate solution space is discreet but continuous-space solvers are fast and convenient. Then as soon as you get within half of discretization step you get an exact solution.