scholarly journals Dykstra′s Alternating Projection Algorithm for Two Sets

1994 ◽  
Vol 79 (3) ◽  
pp. 418-443 ◽  
Author(s):  
H.H. Bauschke ◽  
J.M. Borwein
Keyword(s):  
Projection Algorithm ◽  
Alternating Projection

scholarly journals A New Iterative Algorithm for Solving a Class of Matrix Nearness Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Xuefeng Duan ◽  
Chunmei Li
Keyword(s):  
Iterative Algorithm ◽  
Projection Algorithm ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Von Neumann ◽  
Numerical Examples ◽  
Matrix Nearness Problem ◽  
Least Frobenius Norm Solution ◽  
Alternating Projection ◽  
The Matrix

Based on the alternating projection algorithm, which was proposed by Von Neumann to treat the problem of finding the projection of a given point onto the intersection of two closed subspaces, we propose a new iterative algorithm to solve the matrix nearness problem associated with the matrix equations AXB=E, CXD=F, which arises frequently in experimental design. If we choose the initial iterative matrix X0=0, the least Frobenius norm solution of these matrix equations is obtained. Numerical examples show that the new algorithm is feasible and effective.

scholarly journals Relaxed ordered subset preconditioned alternating projection algorithm for PET reconstruction with automated penalty weight selection

2017 ◽  
Vol 44 (8) ◽  
pp. 4083-4097 ◽  
Author(s):  
C. Ross Schmidtlein ◽  
Yizun Lin ◽  
Si Li ◽  
Andrzej Krol ◽  
Bradley J. Beattie ◽  
...  
Keyword(s):  
Projection Algorithm ◽  
Alternating Projection ◽  
Pet Reconstruction ◽  
Penalty Weight
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