matlab

Math 105LA Computer Assignment 1

Due Sun 10/7, 11pm

a) Write a MATLAB function that implements the bisection method in Algo- rithm 2.1. Make sure that you use the *same order* of input below:

function p = bisection(f,a,b,TOL,N0) % f is the function f % your implementation here end

The ’p’ variable calculated in step 3 will be returned (function p = bisection).

Submit a single file named by your student ID (e.g. huamingy.m) that contains the function. Your code will be tested on a few test cases. Your grade of this assignment depends on the number of cases that your code calculates correctly. Use the example below to test your code. Make sure your code runs without any errors (which results in a zero grade!).

b) Find a root of the equation 6(ex − x) = 7 + 3x2 + 2x3 between −1 and 1 within 10−6 accuracy, using 300 maximum iterations.

First, define an inline function: f = @(x) 6*(exp(x)-x) - (7+3*xˆ2+2*xˆ3); Then, run the following in the command window: bisection(f,-1,1,1e-6,300) and your function should return −0.941764.

Some useful Matlab Commands : 1) If-statement. Use the following code for if x < 0 then y = x2: if x < 0 y = xˆ2; end

2) If-else-statement. Use the following code for if x < 0 then y = x2 else y = cos(x): if x < 0

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y = xˆ2; else y = cos(x); end

3) Various STOP commands. Based on the context, STOP could mean to stop the execution of the algorithm. In this case, use the return command.

Sometimes STOP could also mean to end a for-loop and continue executing the remaining command after the for-loop. For example, use the following code for if x < 0 then STOP FOR LOOP: if x < 0 break end

4) Use the following code to print a line in the command window: disp(’blah blah blah’) To include a variable in the output: n = 3; disp([’blah repeated for’ num2str(n) ’ times.’])

5) Matlab command for ex. exp(x); If x is an array, exp(x) returns an array with each component of x replaced by its exponent.

6) Matlab command for | x | : abs(x); This is also component-wise.

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