scholarly journals Optimal Attitude Determination from Vector Sensors Using Fast Analytical Singular Value Decomposition

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Zhuohua Liu ◽  
Wei Liu ◽  
Xiangyang Gong ◽  
Jin Wu
Keyword(s):  
Singular Value Decomposition ◽  
Attitude Determination ◽  
Computation Time ◽  
Singular Value ◽  
Simulation Experiments ◽  
Vector Sensors ◽  
Vector Observation ◽  
Wahba Problem ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

A novel algorithm is proposed in this paper to solve the optimal attitude determination formulation from vector observation pairs, that is, the Wahba problem. We propose here a fast analytic singular value decomposition (SVD) approach to obtain the optimal attitude matrix. The derivations and mandatory proofs are presented to clarify the theory and support its feasibility. Through simulation experiments, the proposed algorithm is validated. The results show that it maintains the same attitude determination accuracy and robustness with conventional methodologies but significantly reduces the computation time.

Calculation of Fourth-Order Tensor Product Expansion by Power Method and Comparison of it with Higher-Order Singular Value Decomposition

2013 ◽  
Vol 444-445 ◽  
pp. 703-711
Author(s):  
Akio Ishida ◽  
Takumi Noda ◽  
Jun Murakami ◽  
Naoki Yamamoto ◽  
Chiharu Okuma
Keyword(s):  
Singular Value Decomposition ◽  
Tensor Product ◽  
Fourth Order ◽  
Computation Time ◽  
Higher Order ◽  
Singular Value ◽  
Multidimensional Data ◽  
Power Method ◽  
Order Tensor ◽  
Value Decomposition

Higher-order singular value decomposition (HOSVD) is known as an effective technique to reduce the dimension of multidimensional data. We have proposed a method to perform third-order tensor product expansion (3OTPE) by using the power method for the same purpose as HOSVD, and showed that our method had a better accuracy property than HOSVD, and furthermore, required fewer computation time than that. Since our method could not be applied to the tensors of fourth-order (or more) in spite of having those useful properties, we extend our algorithm of 3OTPE calculation to forth-order tensors in this paper. The results of newly developed method are compared to those obtained by HOSVD. We show that the results follow the same trend as the case of 3OTPE.

scholarly journals Some properties of various types of matrix factorization

2021 ◽  
Vol 36 ◽  
pp. 03003
Author(s):  
Wei Shean Ng ◽  
Wei Wen Tan
Keyword(s):  
Pattern Recognition ◽  
Singular Value Decomposition ◽  
Matrix Factorization ◽  
Data Clustering ◽  
Computation Time ◽  
Singular Value ◽  
Cholesky Factorization ◽  
Matrix Factorizations ◽  
Matrix Decompositions ◽  
Value Decomposition

Matrix factorizations or matrix decompositions are methods that represent a matrix as a product of two or more matrices. There are various types of matrix factorizations such as LU factorization, Cholesky factorization, singular value decomposition etc. Matrix factorization is widely used in pattern recognition, image denoising, data clustering etc. Motivated by these applications, some properties and applications of various types of matrix factorizations are studied. One of the purposes of matrix factorization is to ease the computation. Thus, comparisons in term of computation time of various matrix factorizations in different areas are carried out.

Numerical computation of an analytic singular value decomposition of a matrix valued function

1991 ◽  
Vol 60 (1) ◽  
pp. 1-39 ◽  
Author(s):  
Angelika Bunse-Gerstner ◽  
Ralph Byers ◽  
Volker Mehrmann ◽  
Nancy K. Nichols
Keyword(s):  
Singular Value Decomposition ◽  
Numerical Computation ◽  
Singular Value ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

Analytic singular value decomposition of a channeled spectropolarimeter

2001 ◽  
Author(s):  
Derek S. Sabatke ◽  
A.M. Locke ◽  
M.R. Descour ◽  
J.P. Garcia ◽  
E.L. Dereniak ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Analytic Singular Value Decomposition ◽  
Value Decomposition

scholarly journals Cache Servers Placement Based on Important Switches for SDN-Based ICN

Electronics ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 39 ◽  
Author(s):  
Jan Badshah ◽  
Majed Mohaia Alhaisoni ◽  
Nadir Shah ◽  
Muhammad Kamran
Keyword(s):  
Energy Consumption ◽  
Singular Value Decomposition ◽  
Linear Algebra ◽  
Optimization Problem ◽  
Computation Time ◽  
Singular Value ◽  
Qr Factorization ◽  
Traffic Matrix ◽  
Column Pivoting ◽  
Value Decomposition

In centralized cache management for SDN-based ICN, it is an optimization problem to compute the location of cache servers and takes a longer time. We solve this problem by proposing to use singular-value-decomposition (SVD) and QR-factorization with column pivoting methods of linear algebra as follows. The traffic matrix of the network is lower-rank. Therefore, we compute the most important switches in the network by using SVD and QR-factorization with column pivoting methods. By using real network traces, the results show that our proposed approach reduces the computation time significantly, and also decreases the traffic overhead and energy consumption as compared to the existing approach.

Sign in / Sign up

Export Citation Format

Share Document