- Graphic Methods
- Bracketing Methods
- Open Methods
Graphic Methods- No precise load
- Limited Value
- To estimate initial values
- Can prevent failures in the methods (asymptotes)
- Can be considered finite / conditional
Bracketing Methods : Bisection method, The false position method
- Guarantee convergence
- Begins by asking a range (which contient root)
Bisection Method
Search the "cota"(1) and cut the interval by the half
>Binary cut
>Partition
>Bolzano
Types of search
- Define an interval in which at least has a root. The sign change method
- Evaluated the image of the function in the "cotas"(1). The product of these images is below 0
f (a) . f (b) below 0
(If we do not know that there are more "cotas"(1) assume at least 1)
3. Interval is divided in half and is checked, assuming the value on the half is the root.
If f(a)*f(r) below 0
*Repeat as many times as tolerance tells me
4. Tolerance
Advantages- All the bracketing methods converge
- Easy programming
- Has a very clear error handling
Disadvantages
- Convergence may take a long
- Does not take into account extreme values ("cotas") as possible roots.
****(1) What I mean when I write "cota"?
