id	author	title	date	pages	extension	mime	words	sentences	flesch	summary	cache	txt
work_c4s7pkgqufevzob4z575ujo57y	Nicolas Fillion	Numerical Methods, Complexity, and Epistemic Hierarchies	2015	15	.pdf	application/pdf	6644	574	59	mathematical problems that are themselves based on different understandings of computational constraints. numerical values for the solutions are obtainable by computation, which gives In this way, this binary distinction—between mathematical problems that afford exact, explicit solutions and those that do not— exact solution, and it turns out to be closed form since it can be expressed in might turn out that the use of such a formula slows down the actual computation of the result or provides spurious roots due to numerical instability exact solution, in terms of Jacobi elliptic functions, which is closed form. if the exact solution could be captured by ðor given in the form ofÞ an algebraic or elementary expression. uncertainty is always present, this means that our emphasis on an exact solution will not, in general, guarantee the computability of accurate numerical equivalent, both computational costs are linear functions, so the difference We want to use a computed solution from an expression	./cache/work_c4s7pkgqufevzob4z575ujo57y.pdf	./txt/work_c4s7pkgqufevzob4z575ujo57y.txt