File Exchange

## Bisection Method Root Finding

version 1.15 (3.74 KB) by Sky Sartorius

### Sky Sartorius (view profile)

Very simple to use and robust method that takes array inputs, so it even has advantages over fzero.

Updated 20 Feb 2019

BISECTION is a fast, simple-to-use, and robust root-finding method that handles n-dimensional arrays.

Additional optional inputs and outputs for more control and capabilities that don't exist in other implementations of the bisection method or other root finding functions like fzero.
This function really shines in cases where fzero would have to be implemented in a loop to solve multiple cases, in which case this will be much faster.

It can find zero or non-zero roots.

This code can be a bit cryptic. This is for the sake of speed and increased capability. See the many acknowledged other submissions for simpler, easier-to-follow implementations to understand the basics of the bisection method.

### Cite As

Sky Sartorius (2019). Bisection Method Root Finding (https://www.mathworks.com/matlabcentral/fileexchange/28150-bisection-method-root-finding), MATLAB Central File Exchange. Retrieved .

Sky Sartorius

### Sky Sartorius (view profile)

tbaracu: The function requires at least three inputs, e.g. bisection(@cos,-3,3).

tbaracu

### tbaracu (view profile)

It doesn't work:

>> bisection
Not enough input arguments.

Error in bisection (line 115)
ub_in = ub; lb_in = lb;

robert

Tim DeWolf

Gail Gutierrez

### Gail Gutierrez (view profile)

Great Function!!!

David Vicente

Thomas

praydz 96

MK

Herbert

Ole

### Ole (view profile)

If there are several root in the interval does it find the first closes to LB only ?

Chi-Fu

### Chi-Fu (view profile)

great program, saved me a lot of time, thank you!

SiddharthKrishnamoorthy

### SiddharthKrishnamoorthy (view profile)

The vectorization feature is really really helpful. I was vexed with having to put fzero into for loops.

Philip Ohnewein

### Philip Ohnewein (view profile)

Works brilliantly in my case. Replaces a loop with ~1 million iterations, brings down execution time by several orders of magnitude.
Plus it is well-written and well-documented and a numerically robust method.

Fabian

### Fabian (view profile)

Excellent file. Much faster than using fzero in a long loop!

Siegmar W

### Siegmar W (view profile)

Thanks! Had a similar file of my own, but yours is better!

Umberto Picchini

### Umberto Picchini (view profile)

I am so glad I found this submission and I'm very grateful to the author for providing an excellent, well-documented code. I had my custom Newton-Raphson algorithm (with provided analytical gradient) invoked thousands of times inside a for loop. I substituted the loop with a single invocation to bisection.m and achieved a 15x acceleration! Awesome.

Sky Sartorius

### Sky Sartorius (view profile)

I just uploaded an entirely new function with almost all new code and documentation and a lot of added features. With so much new code, please let me know if you find a bug.

This is about as far as I'll take this function. I would love to see MathWorks or someone in the community develop a vectorized implementation of Brent's method, i.e. make FZERO vectorized to be able handle array problems. A vectorized FZERO (with a TolFun feature) would be superior to this in every way.

Yoshiaki

### Yoshiaki (view profile)

There seems to be a typo on line 80:
jnk = f(UB+LB)/2; % test if f returns multiple outputs

It should be
f((UB+LB)/2)

Matthew

### Matthew (view profile)

Excellent documentation with example. Simple function that works as advertised.