I have a function $e^{-rt}$, defined on some interval $[a,b]$, and I want to integrate this function via Chebyshev nodes to some precision $\delta$. How would I go about finding the number of nodes required to do this?
It's clear to see how to transfer the standard $n$ Chebyshev nodes on $[-1,1]$ to $[a,b]$ via an affine transformation (like in this question), but I'm totally lost on how to figure out how many I need.
Also, any good book recommendations to learn more on this topic would be very helpful. I've been learning this stuff ad-hoc for a programming project I'm working on, and I'd like to learn it properly.