Loubignac iteration
Loubignac iteration is a method of solving a type of math problem called a nonlinear equation. Imagine you have two numbers, let's say 2 and 3, and you want to find a third number that, when you add it to 2 and square the result, gives you 3. This is a nonlinear equation because you can't solve it by just adding, subtracting, multiplying, or dividing the numbers you already have.
The Loubignac iteration method is a way to solve this type of equation by making a guess at a possible answer, then using some fancy math to improve your guess until you get really close to the actual answer. Let's say you guess that the third number is 1. You would plug this guess into the equation and see what you get: (2+1)^2 = 9, which is not equal to 3.
Now comes the fancy math part. You take the difference between your guess and the actual answer (in this case, 1-√1 = 0) and divide it by another number (in this case, 2*3+1 = 7). This gives you a small number (.0.1428...) that you can add to your original guess to get a new guess (in this case, 1+0.1428... = 1.1428...).
You repeat this process over and over again, using your newest guess to plug back into the equation and get another tiny adjustment, until your answer is really close to the actual answer (in this case, 1.73205080757...). Congratulations, you just solved a nonlinear equation using Loubignac iteration!
The Loubignac iteration method is a way to solve this type of equation by making a guess at a possible answer, then using some fancy math to improve your guess until you get really close to the actual answer. Let's say you guess that the third number is 1. You would plug this guess into the equation and see what you get: (2+1)^2 = 9, which is not equal to 3.
Now comes the fancy math part. You take the difference between your guess and the actual answer (in this case, 1-√1 = 0) and divide it by another number (in this case, 2*3+1 = 7). This gives you a small number (.0.1428...) that you can add to your original guess to get a new guess (in this case, 1+0.1428... = 1.1428...).
You repeat this process over and over again, using your newest guess to plug back into the equation and get another tiny adjustment, until your answer is really close to the actual answer (in this case, 1.73205080757...). Congratulations, you just solved a nonlinear equation using Loubignac iteration!