Fixed point iteration

Fixed point iteration is like playing a game of "guess what number I'm thinking of" with a calculator. Instead of a number, you have a mathematical equation that needs to solve for its variables.

Here's how it works: you put the equation into the calculator, and then you guess a number for one of the variables. You plug that number back into the equation and it gives you a new number. You then take that new number and plug it back into the equation, and it gives you yet another new number. You keep doing this over and over again until you get two numbers that are really, really close to each other.

When you get two numbers that are very close to each other, you have found the fixed point of the equation. Just like the point on a map that doesn't move, the fixed point of an equation is a value that remains the same no matter how many times you plug it back in.

Using fixed point iteration is a bit like taking baby steps towards the answer, getting closer and closer each time. It might not be the fastest way to solve an equation, but sometimes it's the only way to get there.