https://blogs.mathworks.com/cleve/2019/01/18/floating-point-arithmetic-before-ieee-754

]]>— Cleve ]]>

— Cleve ]]>

which carries the load p = -u”. The integral of p and the Green’s function G(x,x_i), a triangle with a peak at x_i, is the deflection u(x_i) at node x_i. Let w_h = w_i x^i the interpolating function then the integral of -w_h” and G(y,x_i) must be u(x_i) at the nodes. But the second derivatives of the trial functions, ~ x^(i-2) (the loads), are concentrated near the end points and this nearly local character makes them ill-fit for the task and so only wild swings in the coefficients w_i will guarantee w_h(x_i) = u(x_i) ~ 0 in the end zones. ]]>

— Cleve ]]>

https://archive.org/stream/zeitschriftfrma12runggoog#page/n255/mode/2up

A good analysis of Runge’ s paper is contained in chapter 13 of Nick Trefethen’s book on approximation theory: http://bookstore.siam.org/ot128/ ]]>