ELI5: Explain Like I'm 5

Conjugate residual method

Okay kiddo, do you remember learning about solving math problems where you have to find a missing number? Well, sometimes in big math problems, we have so many missing numbers that it can be really hard and take a long time to solve.

The conjugate residual method is a special way to solve these kinds of problems faster. It's like a secret code that helps us find the missing numbers without having to go through all the steps we would normally have to do.

Here's how it works. Let's say we have a really big math problem with lots of missing numbers, and we want to use the conjugate residual method to solve it.

First, we pick a starting point - this is like our "guess" for one of the missing numbers. Then, we use the information we have about the problem to make a second guess for another missing number.

But we don't just guess randomly - we use a special rule that helps us make these guesses in a specific way. This rule is called the "conjugate" rule. When we use this rule, it helps us make our guesses in a way that gets us closer to the correct answer each time.

Now, remember how I said that some math problems can take a really long time to solve? Well, the conjugate residual method helps us solve these problems faster by only making a certain number of guesses instead of having to try solving the whole problem all at once. Each time we make a guess, we get closer and closer to the answer until we finally figure out all the missing numbers.

And that's how the conjugate residual method works, kiddo! It's like a secret code that helps us solve big math problems faster by making calculated guesses and using a special rule to get closer to the answer each time.