In the bisection method, the absolute error is only halved at each step, making this quantity linear and thus relatively slow compared to Newton's method.
"Molecular" methods alter this quantity by using Wynn's epsilon algorithm and Levin's u method. A non-linear method for altering this quantity takes the nth term of a sequence and rewrites it as the sum of the "A sub n plus one, minus A sub n plus one, minus A sub n squared, over A sub n, plus negative 2 A sub n, plus A sub n minus one." That technique, the Shanks Transformation, is very similar to Aitken's delta-squared process, which also alters this quantity. This quantity is often prefixed with the letter "q" if it is calculated by dividing two terms. The Richardson Extrapolation is often used to increase this quantity for quadrature methods, such as Romberg's algorithm. In the bisection method, the absolute error is only halved at each step, making this quantity linear and thus relatively slow compared to Newton's method. For 10 points, give this quantity, the speed at which a series approaches the limit.
"Molecular" methods alter this quantity by using Wynn's epsilon algorithm and Levin's u method.
rate of convergence [prompt on convergence; prompt on runtime]