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For some problems the error might be small enough or the computation can be resumed some more until the approximation is satisfactory for the particular problem's needs.
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The dipole approximation is developed using the approximation of a flat semi-infinite medium.
The big approximation is your approximation to the problem you want to solve.
The resulting approximation is.
The second approximation is.
This stencil allows the limiter to avoid discontinuities, and in case extremas cannot be avoided, the accuracy of the UNO limiter decreases until a non-oscillatory approximation is obtained.
The reverse of approximation is separation.
The chi-square approximation is asymptotically correct for large samples.
Hence, the geometric mean approximation is conservative.
I always say that approximation is the death of theatre.
This, to a first approximation, is the secular story of our creation.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
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CEO of Professional Science Editing for Scientists @ prosciediting.com