"This applies to both direct and approximate methods."
I think it should read "This applies to both direct and approximate method". There are two methods, of which one is direct and one approximate. So is this sentence in question correct or not? I think it would be fine if we were talking about two groups of methods, of which one would have been direct and one approximate, am I right?
To use the singular "method", you will need "a" in front of the adjectives. As it is, the plural is fine - there are two methods being referred to.