Show transcribed image text Pseudocode, the Bisection method, and the Newton-Raphson method are the basis of this assignment. You are working for DOWN THE TOILET COMPANY that makes floats for ABC commodes. The floating ball has a specific gravity Gs of 0.6 and has a radius R of 5.5 cm. Bisection Method = a numerical method in Mathematics to find a root of a given function. Rough description (pseudo code) of the Bisection Method:.
. Welcome. Basics. Plots and GUI. Applications. Other. Bisection Method - Half-interval Search This code calculates roots of continuous functions within a given interval and uses the Bisection method.
![Algorithm Algorithm](https://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Bisection_method.svg/250px-Bisection_method.svg.png)
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The program assumes that the provided points produce a change of sign on the function under study. If a change of sign is found, then the root is calculated using the Bisection algorithm (also known as the Half-interval Search). If there is no change of sign, an error is displayed. You could try with other low or high values, or you could improve the code to find two values with a different sign before going on.
In general, when we work with numerical methods we must be aware that errors may result for a number of reasons. First, a root may be calculated when it should not be. It could happen if a point is so close to zero that a root is found due to round-off error.
Second, two roots may be so close together that the program never finds the opposite signs between them. You will provide the function, the interval (both low and high values) and a tolerance. This suggested version of the method will list the evaluated intervals and the final approximation found using your tolerance. Function m = bisection(f, low, high, tol) disp( 'Bisection Method' );% Evaluate both ends of the interval y1 = feval(f, low); y2 = feval(f, high); i = 0;% Display error and finish if signs are not different if y1. y2 0 disp( 'Have not found a change in sign. Will not continue.'
); m = 'Error' return end% Work with the limits modifying them until you find% a function close enough to zero.