MATLAB/PYTHON:Parts (d) and (e) onlyPlease show all the steps as much as possibleBe sure to follow the instructionsMatlab code:function root = find_root_trisection(f, a, b, tol, max_iter) if f(a) * f(b) > 0 error('The function does not change sign in the given interval [a, b].'); end for i = 1:max_iter dx = (b - a) / 3; x1 = a + dx; x2 = b - dx; if abs(f(x1)) < tol root = x1; return; end if abs(f(x2)) < tol root = x2; return; end if f(x1) * f(a) < 0 b = x1; else a = x1; end if f(x2) * f(b) < 0 a = x2; end end error('Failed to converge to a root after %d iterations.', max_iter);end------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Python code:def find_root_trisection(f, a, b, tol=1e-6, max_iter=100): if f(a) * f(b) > 0: raise ValueError("The function does not change sign in the given interval [a, b].") for i in range(max_iter): dx = (b - a) / 3 x1 = a + dx x2 = b - dx if abs(f(x1)) < tol: return x1 if abs(f(x2)) < tol: return x2 if f(x1) * f(a) < 0: b = x1 else: a = x1 if f(x2) * f(b) < 0: a = x2 raise Exception(f"Failed to converge to a root after {max_iter} iterations.") Problem 3:I asked ChatGPT to produce code to perform the trisectionmethod - i.e. the bisection method from class, but splitting in to three intervals each timerather than two. The produced code (in Python and Matlab) can be found on Blackboard.(a) Let f(x) = x5-3x+1. Argue (theoretically) that there is a root of this polynomialin [0, 1].(b) Comment the code (in Python or Matlab, your pick) and specify which stoppingprocedure(s) is/are being used. Check that no errors exist in the code. Submit yourcommented code as part of your solution.(c) Run the code (in Python or Matlab, your pick) to try to find a root of f in [0, 1]. Youcan use the default stopping procedure(s) in the code.(d) Which do you think is typically more efficient, the 'bisection method' or the 'trisectionmethod'. Why?(e) Let g(x) = x³ +10.5x¹+2.6525x³-22.2375x²+12.24x-1.35. By plotting g(x) (youdon't have to submit this plot), argue why we might have to be careful with runningthe bisection/trisection method on the interval [0, 1].

Algorithm for Trisection Method for Root Finding:1. Define the function f(x) that you want to find…

MATLAB/PYTHON: Parts (d) and (e) only Please show all the steps as much as possible Be sure to follow the instructions Matlab code: function root = find_root_trisection(f, a, b, tol, max_iter) if f(a) * f(b) > 0 error('The function does not change sign in the given interval [a, b].'); end for i = 1:max_iter dx = (b - a) / 3; x1 = a + dx; x2 = b - dx; if abs(f(x1)) < tol root = x1; return; end if abs(f(x2)) < tol root = x2; return; end if f(x1) * f(a) < 0 b = x1; else a = x1; end if f(x2) * f(b) < 0 a = x2; end end error('Failed to converge to a root after %d iterations.', max_iter); end --------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------- Python code: def find_root_trisection(f, a, b, tol=1e-6, max_iter=100): if f(a) * f(b) > 0: raise ValueError("The function does not change sign in the given interval [a, b].") for i in range(max_iter): dx = (b - a) / 3 x1 = a + dx x2 = b - dx if abs(f(x1)) < tol: return x1 if abs(f(x2)) < tol: return x2 if f(x1) * f(a) < 0: b = x1 else: a = x1 if f(x2) * f(b) < 0: a = x2 raise Exception(f"Failed to converge to a root after {max_iter} iterations.")

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Concept explainers

Question

MATLAB/PYTHON:

Parts (d) and (e) only
Please show all the steps as much as possible
Be sure to follow the instructions

Matlab code:

function root = find_root_trisection(f, a, b, tol, max_iter)
if f(a) * f(b) > 0
error('The function does not change sign in the given interval [a, b].');
end

for i = 1:max_iter
dx = (b - a) / 3;

x1 = a + dx;
x2 = b - dx;

if abs(f(x1)) < tol
root = x1;
return;
end

if abs(f(x2)) < tol
root = x2;
return;
end

if f(x1) * f(a) < 0
b = x1;
else
a = x1;
end

if f(x2) * f(b) < 0
a = x2;
end
end

error('Failed to converge to a root after %d iterations.', max_iter);
end

---------------------------------------------------------------------------------------------------------------

Python code:

def find_root_trisection(f, a, b, tol=1e-6, max_iter=100):
if f(a) * f(b) > 0:
raise ValueError("The function does not change sign in the given interval [a, b].")

for i in range(max_iter):
dx = (b - a) / 3

x1 = a + dx
x2 = b - dx

if abs(f(x1)) < tol:
return x1

if abs(f(x2)) < tol:
return x2

if f(x1) * f(a) < 0:
b = x1
else:
a = x1

if f(x2) * f(b) < 0:
a = x2

raise Exception(f"Failed to converge to a root after {max_iter} iterations.")

Problem 3:
I asked ChatGPT to produce code to perform the trisection
method - i.e. the bisection method from class, but splitting in to three intervals each time
rather than two. The produced code (in Python and Matlab) can be found on Blackboard.
(a) Let f(x) = x5-3x+1. Argue (theoretically) that there is a root of this polynomial
in [0, 1].
(b) Comment the code (in Python or Matlab, your pick) and specify which stopping
procedure(s) is/are being used. Check that no errors exist in the code. Submit your
commented code as part of your solution.
(c) Run the code (in Python or Matlab, your pick) to try to find a root of f in [0, 1]. You
can use the default stopping procedure(s) in the code.
(d) Which do you think is typically more efficient, the 'bisection method' or the 'trisection
method'. Why?
(e) Let g(x) = x³ +10.5x¹+2.6525x³-22.2375x²+12.24x-1.35. By plotting g(x) (you
don't have to submit this plot), argue why we might have to be careful with running
the bisection/trisection method on the interval [0, 1].

Expert Solution

Step by step

Solved in 5 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.