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What numerically unstable algorithms are ever performed with geolocations? Moreover, given the author's point that real measurement errors exceed the false pre
by Majromax 7y ago
What numerically unstable algorithms are ever performed with geolocations?
Moreover, given the author's point that real measurement errors exceed the false precision of published data, if such a calculation were performed and did provide "arbitrarily large" error, it would indicate that the result should in fact be nonsense.
- whatshisface 7y agoI'm thinking about the case where a calculation extends across many roundings.
- Majromax 7y agoThat doesn't necessarily make the algorithm unstable. See for example: >>> import numpy as np >>> x0 = np.random.rand(1) >>> x_rnd = np.round(100*x)/100.0 >>> for i in range(1000): ... x = np.mod(x+np.pi,1) ... x_rnd = np.mod(x_rnd + np.pi,1) ... x_rnd = np.round(100*x)/100 ... >>> x_real = np.mod(x0+1000*np.pi,1) >>> print(x_real,x,x_rnd) (array([0.51013166]), array([0.51013166]), array([0.51])) Note no loss of accuracy for all of the intermediate roundings. The accuracy is preserved because there's no mechanism here to amplify the error. That's why I ask about the kind of algorithms typically applied to geolocated data. Off the top of my head, I can't think of anything that would be both useful and error-amplifying.
- jhayward 7y agoVincenty's formula has some instabilities/failure to converge at certain areas of the globe. [1] https://en.wikipedia.org/wiki/Vincenty%27s_formulae https://en.wikipedia.org/wiki/Vincenty%27s_formulae