How to program efficient pattern searches in a list of float numbers?

[malv]

Simple case:
In this list, how to find all occurences of intervals of n adjacent
indexes having at least one list-member with a value between given
limits.
Visualizing the list as a two-dimensional curve, this is like
horizontally dragging a given rectangle over the curve and finding the
x coordinates where the curve passes through the rectangle.(Define such
a x-index coordinate as the left corner of the rectangle.)

More complicated case:
Given a pair of rectangles spaced relatively to each other in a fixed
manner. Drag this rectangle pair horizontally over the above
two-dimensional curve and list the indexes of the occurences where the
curve passes simultaneously through both rectangles.
(Define such a x-index coordinate as the leftmost corner of the
rectangle pair).

These problems can be solved by programming a naive search advancing
index by index. It seems obvious that due to the localized properties
searched for, much more efficient searches should be possible.
After having found the occurence-indexes for one particular rectangle
set, how to find the pattern occurences after changing one or more
rectangle parameters?