N] f is the truncation error
of the generalized Jacobi series.
However, even in the case of Hankel-band-limited functions, the number of degrees of freedom and the truncation error
bounds have not thus far been computed.
A modification method proposed by Sjoberg (1984) allows minimization of the truncation error
, the influence of erroneous gravity data and geopotential coefficients in the least squares sense.
In order to compute the truncation error
we use the Taylor series expansion with a different notation: for t [member of] [R.
1 the composite trapezoidal truncation error
can be bounded by
The averages of normalized truncation errors
In this case, let us consider no error in the geopotential model where the only error source will be the truncation error
of the integral formula.
Key words and phrases: Interpolation error, extremal function, multidimensional sampling theorem, Whittaker-Kotel'nikov-Shannon sampling formula, Paley-Wiener function class, sharp truncation error
upper bound, random fields, Frechet--(semi-) variation, weak Cramer class random fields.
where c [member of] N and the truncation error
is desired quadrature rule of precision nine for the approximate evaluation of and truncation error
committed in this approximation is given by
As a consequence, by taking N terms of the series in (5), we cannot have a truncation error
that is bounded by
The fact that u'' (t) is continuous will be used in determining a bound for the truncation error
This work concerns with the truncation error
for the corresponding sampling expansion.
In solving boundary-value problems, multigrid methods can provide computable estimates of the truncation error
by comparing discretizations on grids of different mesh sizes.
in the Stokes and Vening Meinesz formulae for different order spherical harmonic gravity terms.