We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as ...

in the research, six degrees of freedom hexapod parallel machine tool is studied and investigated. jacobian matrix is developed by cinematic relations differentiation and using weighted coefficient method, dimensional analysis operation is carried out on jacobian matrix. geometric parameters of cartesian robot workspace are optimized, considering a minimum allowable rotation about three axes, a...

We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We study the distribution of singular values for the matrix of regression coefficients and for the matrix of predicted responses. For both matrices, it is found...

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm minimization problem. However, soft-thresholding of singular values leads to the elimination of important information about the sensed matrix. Weighted nucl...

The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use of TLS for solving problems with very ill-conditioned coefficient matrices whose singular values decay...

In this paper, a novel contrast enhancement technique for contrast enhancement of a low-contrast satellite image has been proposed based on the singular value decomposition (SVD) and discrete cosine transform (DCT). The singular value matrix represents the intensity information of the given image and any change on the singular values change the intensity of the input image. The proposed techniq...

Contrary to the continuous-time case, a discrete-time process y can be represented by minimal linear models (see (1.1) below), which may either have a non-singular or a singular D matrix. In fact, models with D = 0 have been commonly used in the statistical literature. On the other hand, for models with a singular D matrix the Riccati difference equation of Kalman filtering involves in general ...

In this paper, we present a fast implementation of the Singular Value Thresholding (SVT) algorithm for matrix completion. A rank-revealing randomized singular value decomposition (RSVD) algorithm is used to adaptively carry out partial singular value decomposition (SVD) to fast approximate the SVT operator given a desired, fixed precision. We extend the RSVD algorithm to a recycling rank reveal...

In this paper, some optimal inclusion intervals of matrix singular values are discussed in the set A of matrices equimodular with matrix A. These intervals can be obtained by extensions of the Gerschgorintype theorem for singular values, based only on the use of positive scale vectors and their intersections. Theoretic analysis and numerical examples show that upper bounds of these intervals ar...

Matrix polynomials appear in many areas of computational algebra, control systems theory, di‚erential equations, and mechanics, typically with real or complex coecients. Because of numerical error and instability, a matrix polynomial may appear of considerably higher rank (generically full rank), while being very close to a rank-de€cient matrix. “Close” is de€ned naturally under the Frobenius ...