2007-08-05, by Ayal Pinkus
Fun with derivatives part 4: Newton iteration to determine the inverse square root -
A while back I came across the trick used in Quake to efficiently approximate the inverse square root (which is
probably needed in a 3D engine to normalize vectors). It is also a nice demonstration on how one could go about
approximating a function by using Newton iteration. That is the subject of this article.
2007-08-05, by Ayal Pinkus
Fun with derivatives part 3: fast convergence of Newton iteration -
Newton iteration is a natural fit for computer algebra systems because you can use the symbolic facilities first
to take the derivative of a function, and then later on use the arbitrary-precision numeric support to get a very
accurate numeric approximation (starting from a sufficiently close guess). Newton iteration can converge very fast,
which you can see in action in this article.
2007-08-05, by Ayal Pinkus
Fun with derivatives part 2: Taylor series expansions -
This short article shows how you one would go about writing one line of code that generates a Taylor series
expansion of a function in Yacas (without using the built-in function).
2007-07-20, by Ayal Pinkus
Fun with derivatives part 1: defining the concept of a derivative in Yacas -
Taking a derivative is one of the mathematical operations that is easily explained to a computer. This article shows how
it can be done with a few lines of code in Yacas. You can also directly try it out, or extend the code to handle
more complex cases.
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