I am behind on MATH3806. I plan to go into the lab early tomorrow morning to get some help with assignment #2. This assignment concerns the methods of finding roots to equations of the type f(x)=0. There are five methods we studied:

Fixed point

This method uses x(n)=g(x(n-1)) to make an iteration.

Bisector method

This method uses two points, one above the x-axis and one point below. So a necessary condition for this method is f(x(0))*f(x(1)) < 0. Then the next point in this iteration is chosen to be the mid point between the two points and then this point is checked to see if it is above or below the x-axis and this point is a new guess point with whichever of the first two points is opposite the x-axis to this new point. This iteration continues until the root point.

Floating Point method

This method also requires two points, one above the x-axis and one point below. So a necessary condition for this method is again that f(x(0))*f(x(1)) < 0. Then this method takes a line between the two points and where the line crosses the x axis is the next point, so it is also an iteration.

The secant method

This method draws a line between the two initial guess, x(0) and x(1) and then extends this line until it crosses the x-axis and make that point the third point then the new point and the nearest of the first two are the next two guess points.

Newton-Raphson Method

This method uses the first derivative at an intial guess x(0) and constructs a line from the point to the x axis using the first derivative as the slop of the line. Where this line crosses the x-axis is used to make the next guess. This method is taught in first year calculus typically.

I spent an hour typing this post and reviewing the section(2.1) in the textbook on the fixed point method. I need to read the rest of chapter 2 still and complete a MATLAB assignment on chapter 2. Tomorrow in the Lab we will be graded on the lab work we do. Next Thursday I have to hand in the assignment.

I am hoping to do some reading tonight of chapter two. I want to put in another hour tonight then go to the lab tomorrow. I will also spend some time tonight read books for my LAWS courses.