Sentence examples for every approximating from inspiring English sources

It is well known that well-posedness is very important for both optimization theory and numerical methods of optimization problems, which guarantees that, for every approximating solution sequence, there is a subsequence which converges to a solution.

(PSVQEP) λ, p has a unique solution x λ, p, i.e., S λ, p) = {x λ, p }; for any sequence {(λ n, p n )} ⊆ Λ × P with (λ n, p n ) → (λ, p), every approximating sequence {x n } for (PSVQEP) λ, p corresponding to {(λ n, p n )} converges to x λ, p. Definition 2.3.

S λ, p) ≠ ∅; for any sequence {(λ n, p n )} ⊆ Λ × P with (λ n, p n ) → (λ, p), every approximating sequence {x n } for (PSVQEP) λ, p corresponding to {(λ n, p n )} has a subsequence which converges to some point of S λ, p).

(PSVQEP) is said to be well-posed if, for every (λ, p) ∈ Λ × P, (i) (PSVQEP) λ, p has a unique solution x λ, p, i.e., S λ, p) = {x λ, p };   (ii) for any sequence {(λ n, p n )} ⊆ Λ × P with (λ n, p n ) → (λ, p), every approximating sequence {x n } for (PSVQEP) λ, p corresponding to {(λ n, p n )} converges to x λ, p.  .

(PSVQEP) is said to be well-posed in the generalized sense if, for every (λ, p) ∈ Λ × P, (i) S λ, p) ≠ ∅;   (ii) for any sequence {(λ n, p n )} ⊆ Λ × P with (λ n, p n ) → (λ, p), every approximating sequence {x n } for (PSVQEP) λ, p corresponding to {(λ n, p n )} has a subsequence which converges to some point of S λ, p).  .

The main novelty in our proof is that a candidate approximation sequence for every approximate control is carefully constructed and is proved to converge exactly to a desired approximate control; the afore-developed linear theory takes crucial role throughout the procedure.

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous.

The equation is called superstable if every approximate solution of is an exact solution.

The equation of homomorphism is stable if every "approximate" solution can be approximated by a solution of this equation.

(S for every approximate fixed point sequence and for every the sequence converges to 0 uniformly with respect to m.

We say a functional equation is stable if, for every approximate solution, there exists an exact solution near it.