scholarly journals Rank-One NMF-Based Initialization for NMF and Relative Error Bounds Under a Geometric Assumption

2018 ◽  
Author(s):  
Zhaoqiang Liu ◽  
Vincent Y.F. Tan
Keyword(s):  
Relative Error ◽  
Error Bounds ◽  
Rank One ◽  
Geometric Assumption

THE ROLES OF A WEAK SINGULARITY AND THE GRID UNIFORMITY IN RELATIVE ERROR BOUNDS

2001 ◽  
Vol 22 (7-8) ◽  
pp. 789-814 ◽  
Author(s):  
Mario Ahues ◽  
Alain Largillier ◽  
Olivier Titaud
Keyword(s):  
Relative Error ◽  
Error Bounds ◽  
Weak Singularity

scholarly journals Counting Decomposable Univariate Polynomials

2014 ◽  
Vol 24 (1) ◽  
pp. 294-328 ◽  
Author(s):  
JOACHIM VON ZUR GATHEN
Keyword(s):  
Finite Field ◽  
Relative Error ◽  
Error Bounds ◽  
Field Characteristic ◽  
Univariate Polynomials ◽  
Univariate Polynomial

A univariate polynomial f over a field is decomposable if it is the composition f = g ○ h of two polynomials g and h whose degree is at least 2. We determine an approximation to the number of decomposables over a finite field. The tame case, where the field characteristic p does not divide the degree n of f, is reasonably well understood, and we obtain exponentially decreasing relative error bounds. The wild case, where p divides n, is more challenging and our error bounds are weaker.

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