Question

Consider an iteration where in the kth step the minimum is known to lie in the. interval [aₖ ,bₖ]. How many equal sized subintervals should you sub-divide the interval?

Answer 1

The number of equal-sized subintervals to sub-divide the interval depends on the desired precision and the range of the interval being considered.

Step-by-step explanation:

In the given scenario, where the minimum is known to lie in the interval [aₖ, bₖ], the number of equal-sized subintervals to sub-divide the interval depends on the level of precision required. If a higher level of precision is desired, then a greater number of subintervals should be used. Conversely, if a lower level of precision is acceptable, then a smaller number of subintervals can be used.

For example, if the interval [aₖ, bₖ] is divided into n equal-sized subintervals, each subinterval would have a width of (bₖ - aₖ)/n. The smaller the width, the higher the precision.

Ultimately, the number of equal-sized subintervals to sub-divide the interval depends on the desired precision and the range of the interval being considered.