Sentence examples for iteration function from inspiring English sources

However, the Newton iteration of the p-Laplace equation is not discussed in detail in their study, which is very dependent on selection of initial iteration function and also requires an exploratory reduction in the iterative step length (the default step length is 1; see [11]).

In Section 2, we derive an iteration function for polar decomposition.

According to the Newton iteration with step (alpha=1), we obtain the numerical iteration function (u_{1}), depicted on the left-hand side of Figure 2.

We apply Corollary 2.9 to the iteration function ({T^{(N)} colon D_{N} subset mathbb{K}^{n} to mathbb{K}^{n}}) defined by Definition 1.3 and to the function ({E colon mathbb{K}^{n} to mathbb{R}_) defined by (4.1).

We apply Theorem 2.8 to the iteration function ({T^{(N)} colon D_{N} subset mathbb{K}^{n} to mathbb{K}^{n}}) together with the function ({E colon D_{N} to mathbb{R}_) defined by (5.1).

Recently, Proinov [17 19] has developed a general convergence theory for iterative processes of the type x_{k+1} = Tx_{k}, quad k = 0,1,2,ldots, (2.1) where ({T colon D subset X to X}) is an iteration function in a cone metric space X.

The iteration functions, which is local fractional continuous, is obtained easily within the fractal Lagrange multipliers, which can be optimally determined by the local fractional variational theory [32].

In the following definition, we define a sequence ((T^{(N })_{N = 0}^{infty}) of iteration functions in the vector space (mathbb{K}^{n}).

In order to overcome the ill-posed problem, it is necessary to develop a well-posed condition of the iteration functions.

To the best of our knowledge, a well-posed condition of the iteration functions of finite element-Newton iterations for the p-Laplace equation has not been provided so far.

The detailed numerical results are listed in the form NI/NF/NG/CPU, where NI, NF, NG, CPU denote the number of iterations, function evaluations, gradient evaluations and the time of the CPU in seconds, respectively.