Numerical methods for non-linear least squares

Imagine you have a bunch of numbers that you want to fit into a formula. However, the formula you have is not a straight line like y=mx+b. It's more complicated and curvy, like a rollercoaster. It's called a non-linear formula.

So, you need to find the best values for the parameters in the formula that will make it fit the numbers you have. Finding the best values requires some trial and error, also known as iteration.

Numerical methods for non-linear least squares are used to find the best values for the parameters in a non-linear formula when you have a bunch of data points. The method works by trying different combinations of values for the parameters, calculating how well the formula fits the data with those values, and then adjusting the values based on how well the formula fit.

This process is repeated again and again until the formula fits the data points as closely as possible. The goal is to get the difference between the actual data and the predicted values from the formula, to be as small as possible.

So, it's like trying on different outfits until you find the one that fits you best. With numerical methods for non-linear least squares, we try on different values for the parameters until we find the ones that fit the data best.