The method is shown to be globally convergent without any additional assumption.
We show that the proposed method is globally convergent without any additional assumption.
This article includes an example of a D-generalized metric space to show that a sequence in this setting may be convergent without being a Cauchy sequence.
It is not possible to conceive any type of European education policy (complementary or convergent) without the idea of the EDE as a key core question.
When we solve the OFEE format (Problem 6) with six optimal POD bases, according to the seven steps of implementation of the OFEE format in Section 3.3, we find that the OFEE format at (t=2) is still convergent, without the need to renew the POD basis.
Moreover, without any external validating data, convergent validity, i.e. the convergence of related scales and instruments, cannot be determined.
Numerical results show that the incorporation of such a sub-iteration scheme leads to a convergent solution without needs of move-limits or artificial control parameters.
In this paper, a fourth-order compact and energy conservative difference scheme is proposed for solving the two-dimensional nonlinear Schrödinger equation with periodic boundary condition and initial condition, and the optimal convergent rate, without any restriction on the grid ratio, at the order of O h4+τ2) in the discrete L2-norm with time step τ and mesh size h is obtained.
By Alaoglu's theorem, { f k } has a weak∗ convergent subsequence, without loss of generality, denoted still by { f k }.
So, { ϕ ( x n, x 0 ) } is a convergent sequence, without loss of generality, we can assume that lim n → ∞ ϕ ( x n, x 0 ) = d ≥ 0. In particular, by (1.3), the sequence { ( ∥ x n ∥ − ∥ x 0 ∥ ) 2 } is bounded.
