a, truncate=False, info_dict=None) |
The calculation of the error in the extrapolated value is an
O
process, which is expensive in time and memory. A full
table of intermediate values and derivatives through to O
must
be computed and stored, but this does give a reliable error
estimate.
A faster but less reliable method which estimates the error from the
convergence of the extrapolated value is employed if truncate
is True
. This attempts to estimate the error from the
``truncation error'' in the extrapolation, the difference between
the final two approximations. Using this method avoids the need to
compute an intermediate table of derivatives because the error is
estimated from the behavior of the extrapolated value
itself. Consequently this algorithm is an O
process and only
requires O
terms of storage. If the series converges sufficiently
fast then this procedure can be acceptable. It is appropriate to use
this method when there is a need to compute many extrapolations of
series with similar convergence properties at high-speed. For
example, when numerically integrating a function defined by a
parameterized series where the parameter varies only slightly. A
reliable error estimate should be computed first using the full
algorithm described above in order to verify the consistency of the
results.
If a dictionary is passed as info_dict, then two entries will
be added: info_dict['terms_used']
will be the number of
terms used10.1 and info_dict['sum_plain']
will be the sum of these terms without
acceleration.
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(10.2) |