The Newton-Raphson Method
By DarthVader
Date: 2023-03-28
Topic: 188 see comments
Post views: 797
The Newton-Raphson Method
This method provides a way of finding the ‘roots’ (x-intercepts) of a function by approximation.
Formula:
xn + 1 = xn − yn / y'n
Step 1:
Choose an estimated value for x1 (sometimes written as x0) which is the variable written as xn in the formula above.
Step 2:
Substitute this value into the formula like so:
x1 + 1 = x1 − y(x1) / y'(x1)
where x1 is the estimated value you choose to start with.
This will calculate the next value ( x2 ) to use in the formula for the next step.
Step 3:
Repeat the process simply replacing x1 with the result of the calculation above relabelling x1 as x2, and making sure to substitute the value of x2 into the function and derivative for the next iteration of the process like so:
x2 + 1 = x2 − y(x2) / y'(x2)
Repeat this process until the calculations converge on a value, although it may not always converge. This will give an extremely accurate approximation of the solutions to the equation.
Note:
Try finding two values to substitute into a function to find where the function goes from negative to positive, this indicates an interval where the curve crosses the x-axis hence the location of a solution that can be found using the newton method.
Video: https://youtu.be/iVOsU4tnouk
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