Sentence examples for between the regularized solution from inspiring English sources

The main aim of this paper is to present a general regularization method and investigate the error estimate between the regularized solution and the exact solution.

In addition, the stability estimate between the regularized solution and the exact solution is obtained.

For estimating the errors between the regularized solution and its exact solution, numerical experiments have been carried out.

For discrete ill-conditioned problems, this plot displays an 'L-shape' with a corner point, where a certain balance between the regularized solution and fit to the data is achieved (Hansen et al. 2007).

In order to derive the error estimate between the regularized solution and the exact solution, we replace the original filter (frac{1}{1+alpha^{2}|cosqrt{in}xn}x)|^{2}}) with another filter (frac{1}{1+alpha^{2}|cosqrt{in}in})|^{2}}).

Table 1 Comparison of absolute errors between the regularized solutions (pmb{v_{m}}) of (pmb{m=10^{2}}) and (pmb{m=10^{10}}) ( x, t, s ) Exact value App.

Now we give the convergent error estimate between the exact solution and the regularized solution.

We show the error between the exact solution and the regularized solution at β = − 1 2 ln ϵ.

In the following, we will establish an error estimate between the exact solution and the regularized solution.

The difference between the exact solution and the regularized solution can be divided into two parts: (2.5).

end{aligned} (4.4) For each point of time, let us evaluate the 'relative error' between the exact solution and the regularized solution, which is defined by operatorname{RE} varepsilon,t) = frac{{Vert {{u^{re}}(cdot,t) - {u^{ex}}(cdot,t)} Vert }}{{Vert {{u^{ex}}(cdot,t)} Vert }}.