An Extension of the Matrix Inversion Lemma

1985 ◽  
Vol 6 (3) ◽  
pp. 371-377 ◽  
Author(s):  
Nariyasu Minamide
Keyword(s):  
Matrix Inversion ◽  
The Matrix ◽  
Matrix Inversion Lemma

Generalization of the matrix inversion lemma

1986 ◽  
Vol 74 (7) ◽  
pp. 1050-1052 ◽  
Author(s):  
D.J. Tylavsky ◽  
G.R.L. Sohie
Keyword(s):  
Matrix Inversion ◽  
The Matrix ◽  
Matrix Inversion Lemma

scholarly journals Retrieval of Phytoplankton Pigments from Underway Spectrophotometry in the Fram Strait

2019 ◽  
Vol 11 (3) ◽  
pp. 318 ◽  
Author(s):  
Yangyang Liu ◽  
Emmanuel Boss ◽  
Alison Chase ◽  
Hongyan Xi ◽  
Xiaodong Zhang ◽  
...  
Keyword(s):  
Spatial Resolution ◽  
High Performance ◽  
Matrix Inversion ◽  
Percentage Error ◽  
Fram Strait ◽  
Total Chlorophyll ◽  
Concentration Data ◽  
Inversion Technique ◽  
The Matrix ◽  
Gaussian Decomposition

Phytoplankton in the ocean are extremely diverse. The abundance of various intracellular pigments are often used to study phytoplankton physiology and ecology, and identify and quantify different phytoplankton groups. In this study, phytoplankton absorption spectra ( a p h ( λ ) ) derived from underway flow-through AC-S measurements in the Fram Strait are combined with phytoplankton pigment measurements analyzed by high-performance liquid chromatography (HPLC) to evaluate the retrieval of various pigment concentrations at high spatial resolution. The performances of two approaches, Gaussian decomposition and the matrix inversion technique are investigated and compared. Our study is the first to apply the matrix inversion technique to underway spectrophotometry data. We find that Gaussian decomposition provides good estimates (median absolute percentage error, MPE 21–34%) of total chlorophyll-a (TChl-a), total chlorophyll-b (TChl-b), the combination of chlorophyll-c1 and -c2 (Chl-c1/2), photoprotective (PPC) and photosynthetic carotenoids (PSC). This method outperformed one of the matrix inversion algorithms, i.e., singular value decomposition combined with non-negative least squares (SVD-NNLS), in retrieving TChl-b, Chl-c1/2, PSC, and PPC. However, SVD-NNLS enables robust retrievals of specific carotenoids (MPE 37–65%), i.e., fucoxanthin, diadinoxanthin and 19 ′ -hexanoyloxyfucoxanthin, which is currently not accomplished by Gaussian decomposition. More robust predictions are obtained using the Gaussian decomposition method when the observed a p h ( λ ) is normalized by the package effect index at 675 nm. The latter is determined as a function of “packaged” a p h ( 675 ) and TChl-a concentration, which shows potential for improving pigment retrieval accuracy by the combined use of a p h ( λ ) and TChl-a concentration data. To generate robust estimation statistics for the matrix inversion technique, we combine leave-one-out cross-validation with data perturbations. We find that both approaches provide useful information on pigment distributions, and hence, phytoplankton community composition indicators, at a spatial resolution much finer than that can be achieved with discrete samples.

Electromagnetic modeling of 3-D structures by the method of system iteration using integral equations

Geophysics ◽  
1992 ◽  
Vol 57 (12) ◽  
pp. 1556-1561 ◽  
Author(s):  
Zonghou Xiong
Keyword(s):  
Integral Equations ◽  
Three Dimensional ◽  
Computation Time ◽  
Iterative Solution ◽  
Matrix Inversion ◽  
Electromagnetic Modeling ◽  
Direct Inversion ◽  
Conductivity Structure ◽  
The Matrix ◽  
Earth Conductivity

A new approach for electromagnetic modeling of three‐dimensional (3-D) earth conductivity structures using integral equations is introduced. A conductivity structure is divided into many substructures and the integral equation governing the scattering currents within a substructure is solved by a direct matrix inversion. The influence of all other substructures are treated as external excitations and the solution for the whole structure is then found iteratively. This is mathematically equivalent to partitioning the scattering matrix into many block submatrices and solving the whole system by a block iterative method. This method reduces computer memory requirements since only one submatrix at a time needs to be stored. The diagonal submatrices that require direct inversion are defined by local scatterers only and thus are generally better conditioned than the matrix for the whole structure. The block iterative solution requires much less computation time than direct matrix inversion or conventional point iterative methods as the convergence depends on the number of the submatrices, not on the total number of unknowns in the solution. As the submatrices are independent of each other, this method is suitable for parallel processing.

scholarly journals A hypothesis of state covariance decorrelation effects to partial observability SLAM

2019 ◽  
Vol 14 (2) ◽  
pp. 588 ◽  
Author(s):  
H Ahmad ◽  
N.A Othman ◽  
M M Saari ◽  
M S Ramli ◽  
M M Mazlan ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Matrix Inversion ◽  
Matrix Norm ◽  
Main Element ◽  
Partial Observability ◽  
Localization And Mapping ◽  
The Matrix ◽  
Simulation Results ◽  
Partially Observable

<span>This paper analyze the performance of partial observability in simultaneous localization and mapping(SLAM) problem. The study focuses mainly on the effect of having a decorrelation technique known as Covariance Inflation to the estimation. The matrix inversion will be the main element to be investigated through two conditions with respect to some defined environment namely as unstable partially observable SLAM and partially observable SLAM via matrix norm analysis. For assessment purposes, the Extended Kalman Filter estimation is referred as the estimator to understand how the conditions can influence the results. The simulation results depicted that, the matrix norm is able to determine the efficiency of estimation and is proportional to the uncertainties of the system.</span>

scholarly journals Modified Conjugate Gradient Algorithms for Gram Matrix Inversion of Massive MIMO Downlink Linear Precoding

2019 ◽  
Vol 8 (2S11) ◽  
pp. 2834-2840
Keyword(s):  
Conjugate Gradient ◽  
Massive Mimo ◽  
Mimo Systems ◽  
Mimo System ◽  
Low Complexity ◽  
Matrix Inversion ◽  
Gram Matrix ◽  
Linear Precoding ◽  
Inversion Algorithm ◽  
The Matrix

This paper deals with various low complexity algorithms for higher order matrix inversion involved in massive MIMO system precoder design. The performance of massive MIMO systems is optimized by the process of precoding which is divided into linear and nonlinear. Nonlinear precoding techniques are most complex precoding techniques irrespective of its performance. Hence, linear precoding is generally preferred in which the complexity is mainly contributed by matrix inversion algorithm. To solve this issue, Krylov subspace algorithm such as Conjugate Gradient (CG) was considered to be the best choice of replacement for exact matrix inversions. But CG enforces a condition that the matrix needs to be Symmetric Positive Definite (SPD). If the matrix to be inverted is asymmetric then CG fails to converge. Hence in this paper, a novel approach for the low complexity inversion of asymmetric matrices is proposed by applying two different versions of CG algorithms- Conjugate Gradient Squared (CGS) and Bi-conjugate Gradient (Bi-CG). The convergence behavior and BER performance of these two algorithms are compared with the existing CG algorithm. The results show that these two algorithms outperform CG in terms of convergence speed and relative residue.

scholarly journals Rubber Stiffness Optimization for Floor Vibration Attenuation of a Light Bus Based on Matrix Inversion TPA

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hui Shi ◽  
Wenku Shi ◽  
Changhai Yang ◽  
Guozheng Liu ◽  
Zhaomeng Fan ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Optimization Procedure ◽  
Matrix Inversion ◽  
Vibration Test ◽  
Transfer Path ◽  
Stiffness Optimization ◽  
Market Competitiveness ◽  
Vibration Attenuation ◽  
The Matrix ◽  
Floor Vibration

The NVH characteristics of light buses are a very important performance for market competitiveness. To solve the serious floor vibration of a light bus at speed of 60 km/h and 90 km/h, we first derive the matrix inversion TPA (MITPA) method, and then transfer path contribution is analyzed by applying matrix inversion TPA with TPA model establishment, operational vibration test, and FRF measurement. Next, the energy decoupling rate of the powertrain mount system (PMS) is optimized by rubber stiffness optimization based on the path contribution analysis taking both amplitude and phase into consideration. The optimized natural frequencies and energy decoupling rate indicate that energy decoupling rate (EDR) of each DoF of the powertrain mount system is improved. Finally, to verify the optimization effect, this paper implements an operational vibration test with optimized mount installed. The results indicate that floor vibration of postoptimization is improved significantly compared with that of preoptimization. This paper offers a method for engineers to improve vibration problem of vehicle by combining experimental TPA for identification of dominant paths with optimization procedure.

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