numerical-methods,ode,newtons-method,numerical-stability

Usually you chose the solution that is closest to y(i). The correct solution should satisfy y(i+1)=y(i)+h*f(x(i),y(i)) + O(h²) However, for stiff problems the constant in O(h²) can be very large so that this relation is not as helpful as it seems. If L is the Lipschitz constant of f and...

math,rotation,quaternions,rotational-matrices,numerical-stability

That Wikipedia article is biased. From http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Advantages_of_quaternions as of Apr 18, 2014: When composing several rotations on a computer, rounding errors necessarily accumulate. A quaternion that’s slightly off still represents a rotation after being normalised: a matrix that’s slightly off may not be orthogonal anymore and is harder to convert...

python,numpy,sum,numerical-stability

Short answer: You are seeing the difference between a + b + c + d and (a + b) + (c + d) which because of floating point inaccuracies is not the same. Long answer: Numpy implements pair-wise summation as an optimization of both speed (it allows for easier vectorization)...

c#,floating-point,floating-point-precision,numerical-stability

Because the multiplication to get from [0.0f .. 1.0f] to [0 .. UInt32.MaxValue] can itself be approximative, the order of operations that most obviously has the property you desire is multiply, then clamp, then round. The maximum value to clamp to is the float immediately below 232, that is, 4294967040.0f....

c#,data-type-conversion,slimdx,numerical-stability

If this were my application and I was that concerned about the possible loss of integrity, I would recreate the appropriate methods using the required data types. .Net is a general platform that attempts to solve a majority of problems, but it can't solve them all. Although it may be...