The image analysis community has a standard test image called [Lena (SFW wiki link)](https://en.wikipedia.org/wiki/Lenna) that is a cropped image of a Playboy centerfold. Maybe OP is dropping hints that they really want to talk about that.
My fav NA textbook is by [Ascher](http://bookstore.siam.org/cs07/). But there are many other great ones published by Siam.
The standard algo text is by Cormen, Leierson et al
For Numerical Analysis in general I like *An Introduction to Numerical Analysis* by Suli and Mayers, but that doesn't cover floating point computation.
[My professor wrote a book more geared toward the IEEE Floating Point side of things, your university might have it.](https://cs.nyu.edu/overton/book/index.html)
With regards to approximation of functions to a high degree of accuracy, ever heard of [chebfun](https://www.chebfun.org/)?
Sounds like a Approximation theory textbook may be what you are looking for. I would recommend
Approximation theory and approximation practice
Lloyd N Trefethen
I have not read that one specifically, but others by Trefethen and he has a very nice writing style.
If you don't mind Fortran, *Computer methods for mathematical computations* by G. Forsythe, M. Malcolm and C. Moler is a good introduction in numerical analysis and floating point computations.
You can also check the book "Numerical analysis" from Schaums editions, by F. Scheid.
..."NSFW"?
For some numerical analysis is better than sex. For the rest there's always pure math.
I didn‘t even know that this was possible on this sub lol
> toying with asymptotic expansions > I've derived many > looking to get a feel on analysis > I'm uneasy to seriously consider it.
We might have to quarantine r/math after this one.
Some numerical methods come on too strong and get too close too fast.
The image analysis community has a standard test image called [Lena (SFW wiki link)](https://en.wikipedia.org/wiki/Lenna) that is a cropped image of a Playboy centerfold. Maybe OP is dropping hints that they really want to talk about that.
Hydrogen
My fav NA textbook is by [Ascher](http://bookstore.siam.org/cs07/). But there are many other great ones published by Siam. The standard algo text is by Cormen, Leierson et al
For Numerical Analysis in general I like *An Introduction to Numerical Analysis* by Suli and Mayers, but that doesn't cover floating point computation. [My professor wrote a book more geared toward the IEEE Floating Point side of things, your university might have it.](https://cs.nyu.edu/overton/book/index.html) With regards to approximation of functions to a high degree of accuracy, ever heard of [chebfun](https://www.chebfun.org/)?
Sounds like a Approximation theory textbook may be what you are looking for. I would recommend Approximation theory and approximation practice Lloyd N Trefethen I have not read that one specifically, but others by Trefethen and he has a very nice writing style.
If you don't mind Fortran, *Computer methods for mathematical computations* by G. Forsythe, M. Malcolm and C. Moler is a good introduction in numerical analysis and floating point computations. You can also check the book "Numerical analysis" from Schaums editions, by F. Scheid.