Update NonlinearLeastSquaresSolvers

Author: ChrisRackauckas

docs/src/solvers/NonlinearLeastSquaresSolvers.md

@@ -14,6 +14,8 @@ algorithm (`LevenbergMarquardt`).
 
 ## Full List of Methods
 
+### NonlinearSolve.jl
+
   - `LevenbergMarquardt()`: An advanced Levenberg-Marquardt implementation with the
     improvements suggested in the [paper](https://arxiv.org/abs/1201.5885) "Improvements to
     the Levenberg-Marquardt algorithm for nonlinear least-squares minimization". Designed for
@@ -22,5 +24,40 @@ algorithm (`LevenbergMarquardt`).
     handling of sparse matrices via colored automatic differentiation and preconditioned
     linear solvers. Designed for large-scale and numerically-difficult nonlinear least squares
     problems.
-  - `SimpleNewtonRaphson()`: Simple Gauss Newton Implementation with `QRFactorization` to
-    solve a linear least squares problem at each step!
+
+### SimpleNonlinearSolve.jl
+
+These methods are included with NonlinearSolve.jl by default, though SimpleNonlinearSolve.jl can be used 
+directly to reduce dependencies and improve load times. SimpleNonlinearSolve.jl's methods excel at small 
+problems and problems defined with static arrays.
+
+  - `SimpleGaussNewton()`: Simple Gauss Newton implementation using QR factorizations for numerical stability.
+
+### FastLevenbergMarquardt.jl
+
+A wrapper over [FastLevenbergMarquardt.jl](https://github.com/kamesy/FastLevenbergMarquardt.jl). Note that
+it is called `FastLevenbergMarquardt` since the original package is called "Fast", though benchmarks
+demonstrate `LevenbergMarquardt()` usually outperforms.
+
+  - `FastLevenbergMarquardtJL(linsolve = :cholesky)`, can also choose `linsolve = :qr`.
+
+### LeastSquaresOptim.jl
+
+A wrapper over [LeastSquaresOptim.jl](https://github.com/matthieugomez/LeastSquaresOptim.jl).
+Has a core algorithm `LeastSquaresOptimJL(alg; linsolve)` where the choices for `alg` are:
+
+- `:lm` a Levenberg-Marquardt implementation
+- `:dogleg` a trust-region dogleg Gauss-Newton
+
+And the choices for `linsolve` are:
+
+- `:qr`
+- `:cholesky`
+- `:lsmr` a conjugate gradient method (LSMR with diagonal preconditioner).
+
+### MINPACK.jl
+
+### Optimization.jl
+
+`NonlinearLeastSquaresProblem`s can be converted into an `OptimizationProblem` and used with any solver of
+[Optimization.jl](https://github.com/SciML/Optimization.jl).