COSC 4364 Numerical Methods Assignment 3 Brief 2025

Instructions: 

• The working code needs to be submitted together with clear instructions on how to run the code (if necessary) to receive credit.
• The code must contain comments briefly describing the steps you implement.
• Write the scripts by hardcoding the inputs according to the problem. DO NOT write scripts that expect user input. 
• The scripts must print out the required output ON THE CONSOLE. Do not save your output in the MATLAB workspace.
• The console/plotted output of the codes together with your observations and learnings from the results need to be submitted as well in the report. The discussion carries significant weight towards the problem credit. Partial credit will be awarded for submitting codes without discussion of the outcome. 

Submissions are to be made via Canvas. In the form of a zip file with a report file in PDF format and code files that are fairly commented. 

Problem 1.

For a continuous function with a single root in the interval [-3,3] using the bisection method with the interval endpoints as starting points, derive how many steps are required to determine the root with an error of at most 

Problem 2. 

How many bisection steps are required for each decimal digit of accuracy? 

Problem 3. 

• Derive a Newton iteration formula for finding a root of f(x) that does not involve  To which value the Newton iterates converge.
• Derive a Newton iteration formula for finding a root of g(x) that does not involve 1 To which value does the Newton iterates converge?

Problem 4. 

Derive a division-free Newton iteration formula for computing the inverse square root of a positive number R.

MATLAB problems

Problem 5. 

Write a MATLAB program not using built-in functions that finds the root of the polynomial in the interval [2,3] by the following methods.

• Bisection
• Regula Falsi
• Modified Regula Falsi,
• Newton
• Secant. 

Use a nested formula for the polynomial evaluation, double precision, and error tolerance for the root of -