On the Approximation of the Full Mass Matrix in the Rotational-Coordinate-Based Beam Formulation

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Wei Fan ◽  
Hui Ren ◽  
Ren Ju ◽  
Weidong Zhu
Keyword(s):  
Jacobian Matrix ◽  
Sparse Matrix ◽  
Mass Matrix ◽  
Current Approach ◽  
Low Rank ◽  
Full Matrix ◽  
Novel Approach ◽  
Dynamic Analyses ◽  
Rank One ◽  
Single Integral

Abstract A novel approach is developed to approximate the full mass matrix in the rotational-coordinate-based beam formulation, which can improve the efficiency of calculating its inverse in dynamic analyses. While the rotational-coordinate-based beam formulation can reduce numbers of elements and generalized coordinates, its mass matrix is a full matrix, such that corresponding Jacobian matrix is also full, and it is time-consuming to calculate its inverse. To increase efficiency of calculating its inverse, the full mass matrix is approximated in this work. Two approximations are adopted: (1) a double integral is approximated by a single integral; and (2) a full matrix is approximated by a sum of several rank-one matrices. Through this way, the approximate mass matrix can be decomposed as a band-diagonal sparse matrix and multiplication of low-rank matrices, and its inverse can be efficiently calculated using Sherman–Woodbury formula. Through this way, the approximate mass matrix can be efficiently calculated. Several numerical examples are presented to demonstrate the performance of the current approach, and its accuracy and efficiency are analyzed.

Subspace based low rank & joint sparse matrix recovery

2014 ◽  
Author(s):  
Sampurna Biswas ◽  
Sunrita Poddar ◽  
Soura Dasgupta ◽  
Raghuraman Mudumbai ◽  
Mathews Jacob
Keyword(s):  
Sparse Matrix ◽  
Low Rank ◽  
Matrix Recovery

scholarly journals Mutual information for low-rank even-order symmetric tensor estimation

2020 ◽  
Author(s):  
Clément Luneau ◽  
Jean Barbier ◽  
Nicolas Macris
Keyword(s):  
Mutual Information ◽  
Finite Rank ◽  
Interpolation Method ◽  
Symmetric Tensor ◽  
Low Rank ◽  
Tensor Factorization ◽  
Adaptive Interpolation ◽  
Odd Order ◽  
Rank One ◽  
Even Order

Abstract We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.

A blind spectrum sensing based on low-rank and sparse matrix decomposition

2018 ◽  
Vol 15 (8) ◽  
pp. 118-125
Author(s):  
Junsheng Mu ◽  
Xiaojun Jing ◽  
Hai Huang ◽  
Ning Gao
Keyword(s):  
Spectrum Sensing ◽  
Sparse Matrix ◽  
Matrix Decomposition ◽  
Low Rank

scholarly journals A Gradient System for Low Rank Matrix Completion

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 51 ◽  
Author(s):  
Carmela Scalone ◽  
Nicola Guglielmi
Keyword(s):  
Sparse Matrix ◽  
Matrix Completion ◽  
Low Rank ◽  
Frobenius Norm ◽  
Gradient System ◽  
Large Matrix ◽  
Rank Matrix ◽  
Matrix Differential Equations ◽  
Low Rank Matrix Completion ◽  
Matrix Differential

In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix X to M, where the distance is measured in the Frobenius norm. A key element in the solution of this matrix nearness problem consists of the use of a constrained gradient system of matrix differential equations. The obtained results, compared to those obtained by different approaches show that the method has a correct behaviour and is competitive with the ones available in the literature.

A Novel Approach to Nanoscale Materials Synthesis Using Industrial Laser Processing of Organosilazane Liquid Precursors

1990 ◽  
Vol 206 ◽  
Author(s):  
Tongsan D. Xiao ◽  
Peter R. Strutt ◽  
Kenneth E. Gonsalves
Keyword(s):  
Ceramic Powder ◽  
Average Diameter ◽  
Current Approach ◽  
Powder Materials ◽  
Materials Synthesis ◽  
Laser Plume ◽  
New Approach ◽  
Novel Approach ◽  
Liquid Precursors ◽  
Short Time

ABSTRACTA new approach has been developed for the synthesis of nanoscale ceramic powder materials from liquid organosilazane precursors. This technique, by exploiting fast kinetic chemical and physical reactions, makes it possible to synthesize significant quantities of material in a relatively short time. In the current approach aerosols of a silazane monomer, (CH3SiHNH)n, (n = 3 or 4), of mol. wt. 280–320, are injected into the beam of a cw industrial CO2 laser to obtain nanoscale ceramic powders. Injection of the aerosol into the laser-beam results in a high-temperature plume. Rapid condensation of the molecular precursor species emerging from the laser plume results in the formation of preceramic polymer particles, with an average diameter of 62 nm. One attractive feature of this process is that 70 wt.% of the liquid precursor is converted into nanoscale powders. Another feature is that only a further 10 wt.% loss occurs during post thermal treatment to form the end-product.

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