There a few cases would define s-numbers, we specify close approximation numbers (alpha_{n}(S)), Gelfand numbers (c_{n}(S)), Kolmogorov numbers (d_{n}(S)) and Tichomirov numbers (d_{n}^(S)).
In order to enhance accuracy, high order polynomials can be specified as local approximation.
The interior of C is specified by the approximation of the smoothed Heaviside function: Hphi (x)=left{begin{array}{cc}1,& phi (x)<-varepsilon 0,& phi (x)>varepsilon frac{1}{2}{varepsilon{phi }+frac{1}{pi}sinrac{1}{pi}sin left(frac{pi phi (x)}{varepsilon}right)right},& mathrm{otherwise}end{array}right.
The final approximation for the specified range of probabilities, however, will just as likely undercount the population as overcount the population.
Recursive segment subdivision is used to keep the approximation error within specified threshold limits.
An approximation error is specified by (sumnolimits_{z = 2}^{infty } {{{left( { - xi } right)^{z} = xi^{2} } mathord{left/ {vphantom {{left( { - xi } right)^{z} = xi^{2} } {left( {1 + xi } right) cong 0}}} right.
The result is a lattice approximation of the specified shape ready for simulation.
Berry-Esséen and related theorems can, in principle, be used to estimate the speed of convergence of the normal approximation to that specified by the central limit theorem [ 20, 22].
A family of implicit one-step algorithms is generated by specifying the polynomial approximation in conjunction with the quadrature formula used for the evaluation of time integrals.
The approach pursued here is to fix a parameter c for the general level of sound intensity and to specify a linear approximation at this level.
Under an incorrectly specified model, i.e. when the approximation error does not vanish, analogous results are also shown.
