Operator Norm-Based Statistical Linearization to Bound the First Excursion Probability of Nonlinear Structures Subjected to Imprecise Stochastic Loading

2022 ◽  
Vol 8 (1) ◽  
Author(s):  
Peihua Ni ◽  
Danko J. Jerez ◽  
Vasileios C. Fragkoulis ◽  
Matthias G. R. Faes ◽  
Marcos A. Valdebenito ◽  
...  
Keyword(s):  
Operator Norm ◽  
Statistical Linearization ◽  
Nonlinear Structures ◽  
Stochastic Loading ◽  
Excursion Probability

scholarly journals Bounding the first excursion probability of linear structures subjected to imprecise stochastic loading

2020 ◽  
Vol 239 ◽  
pp. 106320 ◽  
Author(s):  
Matthias G.R. Faes ◽  
Marcos A. Valdebenito ◽  
David Moens ◽  
Michael Beer
Keyword(s):  
Linear Structures ◽  
Stochastic Loading ◽  
Excursion Probability

scholarly journals Shape preserving design of geometrically nonlinear structures using topology optimization

2019 ◽  
Vol 59 (4) ◽  
pp. 1033-1051 ◽  
Author(s):  
Yu Li ◽  
Jihong Zhu ◽  
Fengwen Wang ◽  
Weihong Zhang ◽  
Ole Sigmund
Keyword(s):  
Topology Optimization ◽  
Geometrically Nonlinear ◽  
Nonlinear Structures ◽  
Shape Preserving

scholarly journals A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 372
Author(s):  
Nishu Gupta ◽  
Mihai Postolache ◽  
Ashish Nandal ◽  
Renu Chugh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Prior Knowledge ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Null Point ◽  
Operator Norm ◽  
Point Problem ◽  
Common Fixed Point Problem ◽  
Split Common Fixed Point

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Distance From Projections to Nilpotents

1995 ◽  
Vol 47 (4) ◽  
pp. 841-851 ◽  
Author(s):  
Gordon W. Macdonald
Keyword(s):  
Operator Norm ◽  
Arbitrary Rank ◽  
Shortest Distance ◽  
Nilpotent Operators ◽  
Rank One

AbstractThe distance from an arbitrary rank-one projection to the set of nilpotent operators, in the space of k × k matrices with the usual operator norm, is shown to be sec(π/(k:+2))/2. This gives improved bounds for the distance between the set of all non-zero projections and the set of nilpotents in the space of k × k matrices. Another result of note is that the shortest distance between the set of non-zero projections and the set of nilpotents in the space of k × k matrices is .

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