There are also results that allow one to deduce the rate of convergence to the limit whose existence is stated in Fekete's lemma if some kind of both superadditivity and subadditivity is present.
42.
Quasi-Monte Carlo has a rate of convergence close to O ( 1 / N ), whereas the rate for the Monte Carlo method is O ( N " 0.5 ).
43.
Under such circumstances x _ { k } converges exponentially fast to the solution of Ax = b, and the rate of convergence depends only on the scaled condition number \ kappa ( A ).
44.
In case 2, the rate of convergence depends on the absolute value of the ratio between the two roots : the farther that ratio is from unity, the more quickly the continued fraction converges.
45.
In particular, it is well known that any discontinuities in a function reduce the rate of convergence of the Fourier series, so that more sinusoids are needed to represent the function with a given accuracy.
46.
The rate of motion on the MTL is much less than the rate of convergence at the plate boundary, making it difficult to distinguish the motion on the MTL from interseismic elastic straining in GPS data.
47.
The rate of convergence is quadratic, meaning roughly that the number of bits of accuracy doubles on each iteration ( so improving a guess from 1 bit to 64 bits of precision requires only 6 iterations ).
48.
On the other hand, if the multiplicity of the root is not known, it is possible to estimate m after carrying out one or two iterations, and then use that value to increase the rate of convergence.
49.
Preconditioners are useful in iterative methods to solve a linear system Ax = b for x since the rate of convergence for most iterative linear solvers increases as the condition number of a matrix decreases as a result of preconditioning.
50.
The application of Aitken's method to fixed-point iteration is known as Steffensen's method, and it can be shown that Steffensen's method yields a rate of convergence that is at least quadratic.
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