A more general definition associates non-negative weight functions ins ( ), del ( ) and sub (, ) with the operations.
12.
Perhaps a more serious overhead to importance sampling is the time taken to devise and program the technique and analytically derive the desired weight function.
13.
The most common case is w ( x ) = 1, as above, but in certain applications a different weight function is desirable.
14.
A weight function \ rho assigns a non-negative number called a "'weight "'to each tile of T.
15.
If we want to find a minimum spanning tree instead, we simply " invert " the weight function by subtracting it from a large constant.
16.
In this case the singularity can be pulled into the weight function w ( x ) and its analytical properties can be used to compute W _ k accurately beforehand.
17.
Typically, the weight function w ( x ) and ranges a, b are chosen for a specific problem, and leads to one of the different forms of the quadrature.
18.
Since the same weight function is generally used for many integrands f ( x ), however, one can afford to compute these W _ k numerically to high accuracy beforehand.
19.
More generally, one can pose the problem of integrating an arbitrary f ( x ) against a fixed " weight function " w ( x ) that is known ahead of time:
20.
Many more optimization problems about all sorts of matroids and weight functions can be solved in this trivial way, although in many cases more efficient algorithms can be found that exploit more specialized properties.
