Iterative rational Krylov algorithm
Okay, so imagine you have a really big math problem that you need to solve, but you don't know the answer yet. It's kind of like trying to figure out what number comes next in a pattern, but this pattern is really long and complicated.
Now, one way you could try to solve this problem is by guessing what the answer might be and then checking to see if you're right. But that's not a very efficient way to do it, especially if the pattern is really long and complicated.
Instead, the iterative rational krylov algorithm is a way to solve this problem by getting closer and closer to the answer, one step at a time. It's kind of like taking small steps towards the answer, so you don't get lost or go too far in the wrong direction.
The way this works is by breaking down the big problem into smaller, more manageable pieces called "vectors." These vectors are like little parts of the pattern that we're trying to solve, and we can use them to figure out what the next number in the pattern might be.
Then, we use something called a "matrix" to help us figure out how to combine these vectors to get closer to the answer. This matrix is like a set of instructions that tell us how to move from one vector to the next, like a map that shows us which way to go.
As we keep taking these small steps and combining the vectors according to the matrix, we get closer and closer to the answer we're looking for. It's like we're following a trail of breadcrumbs, and each vector and each step gets us one step closer to the end of the trail.
So, the iterative rational krylov algorithm is really just a fancy way of solving a big, complicated math problem by taking small steps and using vectors, matrices, and a little bit of guesswork along the way. But by breaking the problem down into smaller pieces and taking it one step at a time, we can get to the answer without getting lost or overwhelmed.
Now, one way you could try to solve this problem is by guessing what the answer might be and then checking to see if you're right. But that's not a very efficient way to do it, especially if the pattern is really long and complicated.
Instead, the iterative rational krylov algorithm is a way to solve this problem by getting closer and closer to the answer, one step at a time. It's kind of like taking small steps towards the answer, so you don't get lost or go too far in the wrong direction.
The way this works is by breaking down the big problem into smaller, more manageable pieces called "vectors." These vectors are like little parts of the pattern that we're trying to solve, and we can use them to figure out what the next number in the pattern might be.
Then, we use something called a "matrix" to help us figure out how to combine these vectors to get closer to the answer. This matrix is like a set of instructions that tell us how to move from one vector to the next, like a map that shows us which way to go.
As we keep taking these small steps and combining the vectors according to the matrix, we get closer and closer to the answer we're looking for. It's like we're following a trail of breadcrumbs, and each vector and each step gets us one step closer to the end of the trail.
So, the iterative rational krylov algorithm is really just a fancy way of solving a big, complicated math problem by taking small steps and using vectors, matrices, and a little bit of guesswork along the way. But by breaking the problem down into smaller pieces and taking it one step at a time, we can get to the answer without getting lost or overwhelmed.