The best strategy for this in my opinion is to always ask “what’s the picture” (as in visualization)? I can’t remember the mechanical rules for say Newton’s met

The best strategy for this in my opinion is to always ask “what’s the picture” (as in visualization)? I can’t remember the mechanical rules for say Newton’s method, but I have the picture of what Newton’s method does in my head. From that, I can quickly work out the algorithm.