Strategies (under construction)

Bisectors

A bisector is an operator that takes a box \([x]\) as input and returns two sub-boxes \(([x]^{(1)},[x]^{(2)})\) that form a partition of \([x]\), that is, \([x]=[x]^{(1)}\cup[x]^{(2)}\). This partition is obtained by selecting one component \([x_i]\) and splitting this interval at some point.

Each bisector implements a specific strategy for chosing the component. The bisection point in the interval is defined as a ratio of the interval width, e.g., a ratio of 0.5 corresponds to the midpoint.

Bisecting each component in turn

(to be completed)

Bisecting the largest component

(to be completed)

Setting different precision for variables

In real-world applications, variables often correspond to physical quantities with different units. The order of magnitude greatly varies with the unit. For example, consider Coulomb’s law:

\[F=k_e\frac{q_1q_2}{r^2}\]

applied to two charges \(q_1\) and \(q_2\) or ~1e-6 coulomb, with a distance \(r\) of ~1e-2 meter. With Coulomb’s contant ~ 1e10, the resulting force will be in the order of 1e2 Newton.

If one introduces Coulomb’s equation in a solver, using a bisector that handles variables uniformly, i.e., that uses the same precision value for all of them, is certainly not adequate.

Each bisector can be given a vector of different precisions (one for each variable) instead of a unique value. We just have to give a Vector in argument in place of a double. For instance, with the round-robin bisector:

	double _prec[]={1e-8,1e-8,1e-4,1};

	Vector prec(4,_prec);

	RoundRobin rr(prec);

Respecting proportions of a box

If you want to use a relative precision that respects the proportion betweeen the interval widths of an “initial” box, you can simply initialize the vector of precision like this:

Vector prec=1e-07*box.diam(); // box is the initial domain

The Smear Function

(to be completed)

Smear function with maximum impact

(to be completed)

Smear function with maximal sum of impacts

(to be completed)

Smear function with maximal normalized impact

(to be completed)

Smear function with maximal sum of normalized impacts

(to be completed)

maximal sum of impacts

Cell buffers

(to be completed)

Cell Stack

(to be completed)

Cell Heap

(to be completed)