Form Of Singular Value Decomposition Research Articles

An improved Kalman filter algorithm for tightly GNSS/INS integrated navigation system.

The Kalman filter based on singular value decomposition (SVD) can sufficiently reduce the accumulation of rounding errors and is widely used in various applications with numerical calculations. However, in order to improve the filtering performance and adaptability in a tightly GNSS/INS (Global Navigation Satellite System and Inertial Navigation System) integrated navigation system, we propose an improved robust method to satisfy the requirements. To solve the issue of large fluctuations in GNSS signals faced by the conventional method that uses a fixed noise covariance, the proposed method constructs a correction variable through the innovation and the new matrix which is obtained by performing SVD on the original matrix, dynamically correcting the noise covariance and has better robustness. In addition, the derived SVD form of the information filter (IF) extends its application. The proposed method has higher positioning accuracy and can be better applied to tightly coupled GNSS/INS navigation simulations and physical experiments. The experimental results show that, compared with the traditional Kalman algorithm based on SVD, the proposed algorithm*s maximum error is reduced by 45.77%. Compared with the traditional IF algorithm, the root mean squared error of the proposed IF algorithm in the form of SVD is also reduced by 4.7%.

Analysis and extension of multiresolution singular value decomposition

This paper presents an analysis of the multiresolution form of singular value decomposition SVD (MR-SVD) and generalizes the analysis into a random multiresolution form of singular value decomposition (R-MR-SVD) with an intrinsic randomness. The core idea behind the proposed transform is to introduce randomness in the computing process based on parameters without which one can neither decompose nor reconstruct the data correctly. The proposed transform inherits the excellent properties of MR-SVD along with its own unique features, which can be useful in many research areas. Image encryption, lossy image compression, and face recognition are the primary applications used to illustrate the practical usage of the proposed transform.

Generalization of Quantification for PLS Correlation

This study proposes a quantification algorithm for a PLS method with several sets of variables. We called the quantification method for PLS with more than 2 sets of data a generalization. The basis of the quantification for PLS method is singular value decomposition. To derive the form of singular value decomposition in the data with more than 2 sets more easily, we used the constraint, a t a + b t b + c t c = 3 not a t a = 1, b t b = 1, and c t c = 1, for instance, in the case of 3 data sets. However, to prove that there is no difference, we showed it by the use of 2 data sets case because it is very complicate to prove with 3 data sets. The keys of the study are how to form the singular value decomposition and how to get the coordinates for the plots of variables and observations.

SINGULAR VALUE DECOMPOSITION AND MATRIX REORDERINGS IN QUANTUM INFORMATION THEORY

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyze the correspondence between quantum states and operations with the help of Jamiołkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations, we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.

Identifying Rate‐Controlling Enzymes in Metabolic Pathways without Kinetic Parameters

AbstractThe flux control coefficients, originally defined by Kacser and Burns, provide a sound theoretical basis for identifying rate‐controlling enzymes in metabolic pathways. However, the calculation of these quantities requires kinetic parameters, which are usually unavailable in practical systems. This article presents a method for evaluating the flux control coefficients by using measurements of metabolite concentrations in a transient state. The basis of this approach is the relationship identified here between transient fluxes and the flux control coefficients. Principal component analysis in the form of singular value decomposition is used to identify such relationships and evaluate the flux control coefficients. The approach does not require kinetic parameters and depends only on the knowledge of pathway stoichiometry, which is generally available.

Use of the Singular Value Decomposition in Regression Analysis

Abstract Principal component analysis, particularly in the form of singular value decomposition, is a useful technique for a number of applications, including the analysis of two-way tables, evaluation of experimental design, empirical fitting of functions, and regression. This paper is a discussion in expository form of the use of singular value decomposition in multiple linear regression, with special reference to the problems of collinearity and near collinearity.