levin
bflevin_u_sum (a, n, n_0) — Function
Estimate sum(a(n), n, n_0, inf) using the
Levin u-transform in bigfloat arithmetic.
bflevin_u_sum attempts to return the sum of the infinite series
with a precision given by the global variable fpprec using bigfloat arithmetic.
See levin_options for options to control this function.
bflevin_u_sum uses an adaptive algorithm to increase both the number of
terms and the bigfloat precision used for internal calculations
until the estimated error is acceptable.
load("levin") loads this function.
See Examples for levin for examples.
See also: fpprec, levin_options, Examples-for-levin.
Function: levin_options
Function bflevin_u_sum attempts to return the sum of an infinite series
with a precision given by the global variable fpprec using bigfloat arithmetic.
bflevin_u_sum uses an adaptive algorithm to increase both the number of
terms used and the bigfloat precision used for internal calculations
until the estimated error is acceptable.
The undeclared array levin_options contains options for controlling bflevin_u_sum.
Note that the subscript values for levin_options are strings.
levin_options[“debug”] — When true, bflevin_u_sum generates additional output. Default: false
levin_options[“min_terms”] — Minimum number of terms used by bflevin_u_sum. Default: 5
levin_options[“max_terms”] — Maximum number of terms used by bflevin_u_sum. Default: 640 (equal to 5*2^7)
levin_options[“min_precision”] — Initial bigfloat precision for bflevin_u_sum. Default: 16
levin_options[“max_precision”] — Maximum bigfloat precision for bflevin_u_sum. Default: 1000
See also: bflevin_u_sum, fpprec.
levin_u_sum (a, n, n_0, nterms, mode) — Function
Estimate sum(a(n), n, n_0, inf) using at most nterms
terms using the Levin u-transform levin_002d1973.
The following values are recognized for the optional argument mode.
If mode is not supplied, it is assumed to be levin_algebraic.
levin_algebraic — The calculation is performed in exact arithmetic. levin_u_sum returns the result.
levin_numeric — The calculation is performed in bigfloat arithmetic.
The return value is a list [result, variance]
where result is the result of the bigfloat calculation,
and variance is in units of 10^(-2*fpprec).
load("levin") loads this function.
See Examples for levin for examples.
See also: levin-1973, Examples-for-levin.