An Efficient Nearest Point Projection Method Based on Improved Newton Iteration

2021 ◽  
pp. 215-228
Author(s):  
Long Qi ◽  
Dongxiang Xie ◽  
Yufei Pang ◽  
Yang Liu ◽  
Jianqiang Chen ◽  
...  
Keyword(s):  
Projection Method ◽  
Newton Iteration ◽  
Nearest Point ◽  
Nearest Point Projection ◽  
Point Projection

scholarly journals Implicit iteration process of nonexpansive non-self-mappings

2005 ◽  
Vol 2005 (19) ◽  
pp. 3103-3110
Author(s):  
Somyot Plubtieng ◽  
Rattanaporn Punpaeng
Keyword(s):  
Hilbert Space ◽  
Convex Subset ◽  
Real Hilbert Space ◽  
Iteration Process ◽  
Nonempty Closed Convex Subset ◽  
Implicit Iteration Process ◽  
Nearest Point ◽  
Nearest Point Projection ◽  
Point Projection ◽  
Implicit Iteration

SupposeCis a nonempty closed convex subset of real Hilbert spaceH. LetT:C→Hbe a nonexpansive non-self-mapping andPis the nearest point projection ofHontoC. In this paper, we study the convergence of the sequences{xn},{yn},{zn}satisfyingxn=(1−αn)u+αnT[(1−βn)xn+βnTxn],yn=(1−αn)u+αnPT[(1−βn)yn+βnPTyn], andzn=P[(1−αn)u+αnTP[(1−βn)zn+βnTzn]], where{αn}⊆(0,1),0≤βn≤β<1andαn→1asn→∞. Our results extend and improve the recent ones announced by Xu and Yin, and many others.

scholarly journals Projections of the sphere graph to the arc graph of a surface

2018 ◽  
Vol 10 (02) ◽  
pp. 245-261
Author(s):  
Brian H. Bowditch ◽  
Francesca Iezzi
Keyword(s):  
Homotopy Class ◽  
Compact Surface ◽  
Fundamental Groups ◽  
Nearest Point ◽  
Bounded Distance ◽  
Nearest Point Projection ◽  
Uniformly Lipschitz ◽  
Point Projection ◽  
Uniformly Bounded

Let [Formula: see text] be a compact surface, and [Formula: see text] be the double of a handlebody. Given a homotopy class of maps from [Formula: see text] to [Formula: see text] inducing an isomorphism of fundamental groups, we describe a canonical uniformly Lipschitz retraction of the sphere graph of [Formula: see text] to the arc graph of [Formula: see text]. We also show that this retraction is a uniformly bounded distance from the nearest point projection map.

scholarly journals Solving Reynolds lubrication equations using closest point projection method

2020 ◽  
pp. 1-32 ◽  
Author(s):  
Elizaveta Vyacheslavovna Zipunova ◽  
Evgeny Borisovich Savenkov
Keyword(s):  
Projection Method ◽  
Closest Point Projection ◽  
Point Projection

Tomography on Point Projection X-Ray Microscope Using CCD Images

1999 ◽  
Vol 5 (S2) ◽  
pp. 352-353
Author(s):  
Sterling P. Newberry
Keyword(s):  
Data Base ◽  
Projection Method ◽  
Data Gathering ◽  
Cone Beam ◽  
Beam Angle ◽  
Laboratory Installation ◽  
X Ray ◽  
Recent Advances ◽  
Point Projection ◽  
Shadow Projection

Recent advances with the cone-beam approach to tomography at the Advanced Microscopy and Imaging Laboratory (AMIL) have opened the possibility of employing tomography with the Shadow Projection X-Ray Microscope routinely when the specimen properties require it. The AMIL approach has been tested on small objects, without magnification, using conventional dental x-ray sources and a modestly diverging beam angle. The shadow projection Microscope, by contrast has a tenfold greater divergence and magnifies the specimen from unity to three or more orders of magnitude in resolution beyond the previous tests. The reader is reminded of the simplicity of the xray projection method and of the clarity of its images in fig. 1 and 2. The microscope can be operated in any laboratory and readily transported to alternate locations. Now that the AMIL data base and algorithms for tomography can be handled by a Pentium II processor the data gathering and reconstructions can also be managed at any laboratory installation.

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