scholarly journals Improved fixed-rank Nyström approximation via QR decomposition: Practical and theoretical aspects

2019 ◽  
Vol 363 ◽  
pp. 261-272 ◽  
Author(s):  
Farhad Pourkamali-Anaraki ◽  
Stephen Becker
Keyword(s):  
Qr Decomposition ◽  
Nyström Approximation ◽  
Fixed Rank

scholarly journals Multipath number estimation based on QR decomposition

2021 ◽  
Vol 1738 ◽  
pp. 012069
Author(s):  
Xiangying Gao ◽  
Zhixin Liu ◽  
Yongjun Zhao ◽  
Chengcheng Liu
Keyword(s):  
Qr Decomposition

scholarly journals On the Ehrhart Polynomial of Minimal Matroids

2021 ◽  
Author(s):  
Luis Ferroni
Keyword(s):  
Ehrhart Polynomial ◽  
Matroid Polytopes ◽  
Connected Matroid ◽  
Fixed Rank

AbstractWe provide a formula for the Ehrhart polynomial of the connected matroid of size n and rank k with the least number of bases, also known as a minimal matroid. We prove that their polytopes are Ehrhart positive and $$h^*$$ h ∗ -real-rooted (and hence unimodal). We prove that the operation of circuit-hyperplane relaxation relates minimal matroids and matroid polytopes subdivisions, and also preserves Ehrhart positivity. We state two conjectures: that indeed all matroids are $$h^*$$ h ∗ -real-rooted, and that the coefficients of the Ehrhart polynomial of a connected matroid of fixed rank and cardinality are bounded by those of the corresponding minimal matroid and the corresponding uniform matroid.

Real-domain QR decomposition models employing zeroing neural network and time-discretization formulas for time-varying matrices

2021 ◽  
Vol 448 ◽  
pp. 217-227
Author(s):  
Zhenyu Li ◽  
Yunong Zhang ◽  
Liangjie Ming ◽  
Jinjin Guo ◽  
Vasilios N. Katsikis
Keyword(s):  
Neural Network ◽  
Time Discretization ◽  
Qr Decomposition ◽  
Time Varying ◽  
Real Domain ◽  
Decomposition Models

scholarly journals A pathological case of the C1 conjecture in mixed characteristic

2018 ◽  
Vol 167 (01) ◽  
pp. 61-64 ◽  
Author(s):  
INDER KAUR
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Projective Curve ◽  
Free Sheaf ◽  
Smooth Projective Curve ◽  
Mixed Characteristic ◽  
Locally Free Sheaf ◽  
Fixed Rank ◽  
Pathological Case

AbstractLet K be a field of characteristic 0. Fix integers r, d coprime with r ⩾ 2. Let XK be a smooth, projective, geometrically connected curve of genus g ⩾ 2 defined over K. Assume there exists a line bundle ${\cal L}_K$ on XK of degree d. In this paper we prove the existence of a stable locally free sheaf on XK with rank r and determinant ${\cal L}_K$. This trivially proves the C1 conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.

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