In fact, the standard Fibonacci sequence provides the best possible rational approximations to the golden ratio for numbers of a given size.
22.
The best rational approximation problem presented here is non-trivial and has both academic interest and possible practical utility besides error-free usage.
23.
However, it is possible to merge the two steps ( rational approximation to the square root operator and discretization of z ) into one step.
24.
Namely, one can find rational approximations to the so-called one-way propagator ( the exponential of the square root operator ) directly.
25.
However, " best rational approximations " with minimal denominators can be derived from the talk ) 00 : 58, 28 January 2010 ( UTC)
26.
In other words, given the irrationality measure ? of a real number " x ", whenever a rational approximation " x"
27.
Nikishin also did research on rational approximations in number theory and wrote a monograph on such approximations in a unified approach that also treated rational approximations in function spaces.
28.
Nikishin also did research on rational approximations in number theory and wrote a monograph on such approximations in a unified approach that also treated rational approximations in function spaces.
29.
Although the problem of the absolute best digit rational approximation is exponential, it is enough if we take 6-or 7-digit absolute best rational approximations.
30.
Although the problem of the absolute best digit rational approximation is exponential, it is enough if we take 6-or 7-digit absolute best rational approximations.
