QR decomposition of matrix is one of the important problems in the field of matrix theory. Besides, there are also so many extensive applications that using QR decomposition. Because of that, there are many researchers have been studying about algorithm for this decomposition. Two of those researchers are Feng Tianxiang and Liu Hongxia. In their paper, they proposed new algorithm to make QR dec...

A QR–method for computing the singular values via semiseparable matrices. Abstract The standard procedure to compute the singular value decomposition of a dense matrix, first reduces it into a bidiagonal one by means of orthogonal transformations. Once the bidiagonal matrix has been computed, the QR–method is applied to reduce the latter matrix into a diagonal one. In this paper we propose a ne...

Lignin is the second most abundant natural biopolymer, and lignin wastes are therefore potentially significant sources for renewable chemicals such as fuel compounds, as alternatives to fossil fuels. Waste valorisation of lignin is currently limited to a few applications such as in the pulp industry, however, because of the lack of effective extraction and characterisation methods for the chemi...

We show that the Fischer-Burmeister complementarity functions, associated to the semidefinite cone (SDC) and the second order cone (SOC), respectively, are strongly semismooth everywhere. Interestingly enough, the proof stems in a relationship between the singular value decomposition of a nonsymmetric matrix and the spectral decomposition of a symmetric matrix.

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different ma...

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided. Keywords—Matrix equation, Generalized inverse, Generalized singular-value decomposition.

Many scientific computing algorithms (in various domains, such as weather prediction, structural analysis, or electrical network analysis) strongly rely on solving fundamental matrix computation problems (such as linear system solving, eigenvalue decomposition, singular value decomposition, matrix nearness problems, joint diagonalization of matrices...). These problems are often solved using it...

We consider parallel computing of the Householder QR decomposition on SMP machines. This decomposition is one of the basic tools in matrix computations and is used in various problems such as the least square problem and the singular value decomposition of a rectangular matrix. Since this algorithm consists almost entirely of BLAS routines such as matrix-vector multiplications, the simplest way...

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

In this paper we study the partial Brauer C-algebras Rn(δ, δ ), where n ∈ N and δ, δ ∈ C. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction Rn−1 →֒ Rn. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.