If your answer for the calc_realmax program is greater than one-half the value returned by MATLAB when you type realmax, you're at least on the right track -- your value has the largest possible exponent. Don't get stuck on finishing this program if it prevents you from answering the rest of the questions.
If you have not already done so, create a directory for this lab and copy the lab 2 files into it. If you start off in your home directory you can do the following:
mkdir ~/cs371/lab2 cd ~/cs371/lab2 cp ~cs371/lab2/* .and (as always) don't forget to type that last period.
2 f(x) = sin(x) + x - 1 .It is usually a good idea, before running any zero-finding algorithm, to take a look at your function and see more or less where the zeros are. Take a look at the program plot_f.m, fill it in where the comments ask you, and see what you get.
It should look like f(x) has a zero somewhere around -1.4 or so and another one around .7 or so.
Now that we have an idea of what f(x) looks like - it looks smooth and fairly simple - we can choose good initial values and expect the Newton-Raphson method to work.
Note that to correctly compute the next step in the Newton-Raphson method, we need the derivative of f(x). Fortunately our f(x) is simple enough to do that algebraically. (I'm leaving that up to you.)
Now look at the program newton.m. Note that this is a MATLAB function instead of a MATLAB script. You will run it by specifying an initial value for it to start with. For example, you would type newton(2) to start with an initial guess of 2.
Finish the program newton.m and answer the corresponding questions on the answer sheet.
The program secant.m is again just a skeleton, and in fact it probably looks almost exactly like the skeleton for newton.m - this should not be surprising at these are fairly similar methods attacking the same problem.
Finish the program secant.m (for the same function f(x) used above) and answer the corresponding questions on the answer sheet.
Feel free to take a crack at the extra credit problem if you want.