MACM 316 COMPUTING ASSIGNMENT #2

Submit on Crowdmark by Tuesday, June 8, 2021, 11:59pm


Instruction

Upload a PDF file with two parts. Part one should include your typed report (your discussions, data and figures). Part two should list your code. You will receive a Crowdmark link for uploading your results.


Implementing equation solving methods

1. Implement the bisection method in Matlab and use it to approximate the real number solution to the following equation.

Please report: (i) what is the initial interval [a0, b0]? why? (ii) are you using middle points or golden ratio points? (iii) the first 11 values of iteration c0, c1, ..., c10.



2. Implement the method of fixed-point iteration in Matlab and use it to approximate the real number solution to the following equation.

Please report: (i) what is the iteration function g(x) that you are using? (ii) what is the initial value p0? why? (iii) the first 11 values of iteration p0, p1, ..., p10.



3. Implement Newton’s method in Matlab and use it to approximate the real number solution to the following equation.

Please report: (i) what is the initial value p0? why? (ii) the first 11 values of iteration p0, p1, ..., p10.



4.Implement the secant method in Matlab and use it to approximate the real number solution to the following equation.

Please report: (i) what is the initial value p0? why? (ii) the first 11 values of iteration p0, p1, ..., p10.



5. Make a table that summarizes the values of first 11 iterations of the four methods and compare the methods. Which of the methods converges fastest?