Sentence examples for a sequence of projections from inspiring English sources

To overcome this difficulty, Fukushima [14] suggested the so-called relaxed projection method to calculate the projection onto a level set of a convex function by computing a sequence of projections onto half-spaces containing the original level set.

To overcome this difficulty, Fukushima [20] suggested a so-called relaxed projection method to calculate the projection onto a level set of a convex function by computing a sequence of projections onto half-spaces containing the original level set.

Since the computation of a projection onto a closed convex subset is generally difficult, to overcome this difficulty, Fukushima [13] suggested a way to calculate the projection onto a level set of a convex function by computing a sequence of projections onto half-spaces containing the original level set.

This technique produces a sequence of projection X-ray images of blood vessels that is used in diagnosis and treatment.

The optimization is restricted to certain subsets of variables, which are the results of a sequence of projection operations related to the matrix of instrumental responses.

Tomosynthesis improves upon conventional geometric tomography in that it allows an arbitrary number of in-focus planes to be generated retrospectively from a sequence of projection radiographs that are acquired during a single sweep of the X-ray tube using reconstruction techniques such as filtered back projection [ 13].

Tsukada [19] proved the following theorem for a sequence of metric projections in a Banach space.

On the other hand, Ibaraki et al. [20] proved the following theorem for a sequence of generalized projections in a Banach space.

Later, Sine [3] gave a simple proof of Theorem 1.2 by applying a version of the uniform boundedness principle and the convex combination of a sequence of metric projections onto closed and convex sets.

If (e_{i}) is an increasing sequence of projections in ℳ converging strongly to 1, we have (lim_{irightarrowinfty}|xe_{i}-x|_{p, omega}=0), (lim_{irightarrowinfty}|e_{i}x-x|_{p, omega}=0), (forall xinLambda_{omega}^{p}(mathcal{M})).

(ii) If (e_{i}) is an increasing sequence of projections in ℳ converging strongly to 1, we have (lim_{irightarrowinfty}|xe_{i}-x|_{p, omega}=0), (lim_{irightarrowinfty}|e_{i}x-x|_{p, omega}=0), (forall xinLambda_{omega}^{p}(mathcal{M})).