Automatically find all roots of a function using bisect method

Question

ILoveMath 2022-4-26

编辑： Sam Chak 2022-4-26

MATLAB using bisection:

Function: -x^4+12x^2-3x-5 Defined on [-4,4]

Write a script to automatically find the intervals [a,b] containing the four roots. Then, plot them.

I have already plotted the function, but am stuck on how to find the roots.

Sam Chak 2022-4-26

编辑：Sam Chak 2022-4-26

@ILoveMath, Can you show the bisection formula in LaTeX and then write it in MATLAB code?

Mathematics is a declarative language that shows the Iteration formula, but generally does not teach "looping".

Does the Lecturer or the Textbook show another formula to automatically find all ROOTS using Bisection iteration formula?

Answer 1

Torsten 2022-4-26

编辑：Torsten 2022-4-26

Choose delta small, e.g. 0.01.

Evaluate f at -4 and at -4+delta.

If f(-4)*f(-4+delta) <=0, there will be a root in between.

If f(-4)*f(-4+delta)>0, continue by setting -4 to -4+delta and -4+delta -> -4+2*delta.

If f(-4+delta)*f(-4+2*delta) <=0, there will be a root in between...