November 2014 Archives

It's All Downhill From Here

Last time we took a look at function optimisation, implementing the bisection and golden section search algorithms to find local minima; the points at which a function returns a smaller value than at any nearby point.

Now this is all fine and dandy, but what if we want to minimise a function that takes two arguments? Or three arguments? Or four, four arguments; mwah, ha, ha, ha, ha!

Er, I seem to be channelling Count von Count. Let me get some garlic...

Full text...  

That Shrinking Feeling

In the last few posts I described the bisection method, Newton's method and the secant method for numerically approximating the inverses of functions. Specifically, given a function f and some target value y these algorithms seek some argument x such that f(x)=y, at least to within some given error threshold.

Related to the problem of inverting functions is the problem of minimising them, in which we seek arguments at which functions return their least values.

Full text...