Investigate the solution of equations, comparing the following methods, Systematic search for change of sign using a decimal search, Fixed point iteration using the Newton-Raphson method, Fixed point iteration after rearranging the equation f(x)=0 into th

The first 200 words of this essay...

Pure Mathematics 2: Component 02 (Coursework)

During this coursework, I intend to investigate the solution of equations, comparing the following methods.

i) Systematic search for change of sign using a decimal search

ii) Fixed point iteration using the Newton-Raphson method

iii) Fixed point iteration after rearranging the equation f(x)=0 into the form x=g(x)

After implementing these three equations to find the same root of the equation, I will compare the methods in terms of speed of convergence and whether available hardware/software simplify the problem.

Change of Sign Method

The equation I intend to use is...

f(x) = x³ - 4x² - 11x +10

When using this equation I am assuming that f(x) = y = 0

This equation cannot be solved by normal algebraical methods, such as factorising, which is why these numerical methods must be used.

Here is an unaltered graph of the line of the equation above.

If y changes sign in an interval, a root lies in between that interval. I know for a fact that there is a root between 0 and 1 as the lines cuts the x-axis (where y=0) somewhere between