scholarly journals Infeasibility and Error Bound Imply Finite Convergence of Alternating Projections

2021 ◽  
Vol 31 (4) ◽  
pp. 2863-2892
Author(s):  
Roger Behling ◽  
Yunier Bello-Cruz ◽  
Luiz-Rafael Santos
Keyword(s):  
Error Bound ◽  
Alternating Projections ◽  
Finite Convergence

scholarly journals On Dykstra’s algorithm: finite convergence, stalling, and the method of alternating projections

2020 ◽  
Vol 14 (8) ◽  
pp. 1975-1987
Author(s):  
Heinz H. Bauschke ◽  
Regina S. Burachik ◽  
Daniel B. Herman ◽  
C. Yalçın Kaya
Keyword(s):  
Alternating Projections ◽  
Finite Convergence ◽  
Method Of Alternating Projections ◽  
Dykstra’S Algorithm

A new approach for optimal offline time-series segmentation with error bound guarantee

2021 ◽  
Vol 115 ◽  
pp. 107917
Author(s):  
Ángel Carmona-Poyato ◽  
Nicolás Luis Fernández-Garcia ◽  
Francisco José Madrid-Cuevas ◽  
Antonio Manuel Durán-Rosal
Keyword(s):  
Time Series ◽  
Error Bound ◽  
New Approach ◽  
Time Series Segmentation

scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

scholarly journals On the error bound in a combinatorial central limit theorem

Bernoulli ◽  
2015 ◽  
Vol 21 (1) ◽  
pp. 335-359 ◽  
Author(s):  
Louis H.Y. Chen ◽  
Xiao Fang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Error Bound ◽  
Central Limit

scholarly journals A variational approach to the alternating projections method

2021 ◽  
Author(s):  
Carlo Alberto De Bernardi ◽  
Enrico Miglierina
Keyword(s):  
Convex Sets ◽  
Nonempty Intersection ◽  
Feasibility Problem ◽  
Alternating Projections ◽  
Limit Sets ◽  
Von Neumann ◽  
Convex Feasibility ◽  
Starting Point ◽  
Method Of Alternating Projections ◽  
Alternating Projections Method

AbstractThe 2-sets convex feasibility problem aims at finding a point in the nonempty intersection of two closed convex sets A and B in a Hilbert space H. The method of alternating projections is the simplest iterative procedure for finding a solution and it goes back to von Neumann. In the present paper, we study some stability properties for this method in the following sense: we consider two sequences of closed convex sets $$\{A_n\}$$ { A n } and $$\{B_n\}$$ { B n } , each of them converging, with respect to the Attouch-Wets variational convergence, respectively, to A and B. Given a starting point $$a_0$$ a 0 , we consider the sequences of points obtained by projecting on the “perturbed” sets, i.e., the sequences $$\{a_n\}$$ { a n } and $$\{b_n\}$$ { b n } given by $$b_n=P_{B_n}(a_{n-1})$$ b n = P B n ( a n - 1 ) and $$a_n=P_{A_n}(b_n)$$ a n = P A n ( b n ) . Under appropriate geometrical and topological assumptions on the intersection of the limit sets, we ensure that the sequences $$\{a_n\}$$ { a n } and $$\{b_n\}$$ { b n } converge in norm to a point in the intersection of A and B. In particular, we consider both when the intersection $$A\cap B$$ A ∩ B reduces to a singleton and when the interior of $$A \cap B$$ A ∩ B is nonempty. Finally we consider the case in which the limit sets A and B are subspaces.

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