Comments on: Spotting sensitivity in an equation http://www.johndcook.com/blog/2012/12/22/spotting-sensitivity-in-an-equation/ John D. Cook Fri, 17 May 2013 17:39:35 +0000 hourly 1 http://wordpress.org/?v=3.5.1 By: Nick Craig-Wood http://www.johndcook.com/blog/2012/12/22/spotting-sensitivity-in-an-equation/comment-page-1/#comment-3948 Nick Craig-Wood Sun, 23 Dec 2012 10:15:48 +0000 http://www.johndcook.com/blog/?p=12647#comment-3948 Your analysis seems to be saying that a 1% error in θ leads to a 2% error in r.

That shouldn’t be a surprise should it? If you knew nothing about numerical analysis then you might guess that a 1% error in the input made a 1% error in the output, so 2% doesn’t seem so surprising.

Or is the surprise that 2% * a big number is still a big number?

]]> By: Francois http://www.johndcook.com/blog/2012/12/22/spotting-sensitivity-in-an-equation/comment-page-1/#comment-3947 Francois Sun, 23 Dec 2012 09:14:16 +0000 http://www.johndcook.com/blog/?p=12647#comment-3947 the -> that

]]> By: Francois http://www.johndcook.com/blog/2012/12/22/spotting-sensitivity-in-an-equation/comment-page-1/#comment-3946 Francois Sun, 23 Dec 2012 09:06:19 +0000 http://www.johndcook.com/blog/?p=12647#comment-3946 Also note the using simple second- and first-order approximations (resp. on the left and right-hand sides) leads to the simple equation
r = 305.1 (2/theta^2)
giving r=6.23824*10^6 (accurate to more than 0.005% if compared to the true solution r=6.23799*10^6).

]]> By: Adam http://www.johndcook.com/blog/2012/12/22/spotting-sensitivity-in-an-equation/comment-page-1/#comment-3945 Adam Sat, 22 Dec 2012 20:09:34 +0000 http://www.johndcook.com/blog/?p=12647#comment-3945 It’s worth noting that its not just the radius which is sensitive but also the log of the radius. That is, the derivative normalized by the radius (1/r)dr/dtheta is still proportional to something big (r/300m or so). This is the more important metric, as it is dimensionless.

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