Sentence examples for minimum norm element from inspiring English sources

As an application, we can find the minimum norm element without involving projection.

In particular, if contains the origin 0, taking, the sequence converges strongly to the minimum norm element in.

In particular, if contains the origin 0, taking, then the sequence generated by (1.14) converges strongly to the minimum norm element in.

Then the sequence ({x_{n}}) generated by algorithm (3.36) converges strongly to (x^=P_{Gamma}(0)x^), which is the minimum norm element in Γ.

Then the sequence { x n } generated by (3.4) converges to a point x ∗ ∈ S which is the minimum norm element in S.

Finally, if we take f = 0, by a similar argument as that in Theorem 3.3, we deduce immediately that x ˜ is a minimum norm element in Γ.

where is the minimum-norm element of (i.e., the projection ).

Due to uniqueness of minimum-norm element, we must have.

Hence it is an interesting problem to find the minimum-norm element without using the projection.

This indicates that x ˜ is the minimum-norm element in S V I ( C, A ).

Due to the uniqueness of a minimum-norm element, we obtain w ˆ = w ˜. □.