Multiplication
Multiplying Intervals is a lot more complicated then adding and subtracting Intervals. To multiply Intervals follow the steps below:
low X=a
high X=b
low Y=c
high Y=d
low result=e
high result=f
A) If a >= 0
1. If c >= 0
a) a * c = e
b) b * d = f
2. If d <= 0
a) b * c = e
b) a * d = f
3. If neither 1 or 2 apply
a) b * c = e
b) b * d = e
B) If b <= 0
1. If c >= 0
a) a * d = e
b) b * c = f
2. If d <= 0
a) b * d = e
b) a * c = f
3. If neither 1 of 2 apply
a) a * d = e
b) a * c = f
C) If neither A of B apply
1. If c >= 0
a) a * d = e
b) b * d = f
2. If d <= 0
a) b * c = e
b) a * c = f
3. If neither 1 or 2 apply
a) e = Minimum of (a * d, b * c)
b) f = Maximum of (a * c, b * d)
| X Values:
| [a,b]
|
| Y Values:
| [c,d]
|
When calculating Intervals the X values are placed "on top of" the Y values. Also the lowest value of either the X of the Y is placed first in the set.
| X Values:
|
| [a,b]
|
| Y Values:
| *
| [c,d]
|
| Result:
|
| [e,f]
|