The normalized eight-point algorithm is broadly used for the computation of the fundamental matrix between two images given a set of correspondences. However, it performs poorly for low-size datasets due to the way in which the rank-two constraint is imposed on the fundamental matrix. We propose two new algorithms to enforce the rank-two constraint on the fundamental matrix in closed form. The ...

We prove an optimal estimate of the smallest singular value of a random subGaussian matrix, valid for all dimensions. For an N n matrix A with independent and identically distributed sub-Gaussian entries, the smallest singular value of A is at least of the order p N pn 1 with high probability. A sharp estimate on the probability is also obtained. © 2009 Wiley Periodicals, Inc.

Abstract. Analogous to the pole assignment problem where eigenvalues of a square matrix are relocated, this paper considers the problem of reassigning singular values of a rectangular matrix by additive low rank matrices. Precise and easy-to-check necessary and sufficient conditions under which the problem is solvable are completely characterized, generalizing some traditional singular value in...

Hankel matrices are an important family of matrices that play a fundamental role in diverse fields of study, such as computer science, engineering, mathematics and statistics. In this paper, we study the behavior of the singular values of the Hankel matrix by changing its dimension. In addition, as an application, we use the obtained results for choosing the optimal values of the parameters of ...

In this paper we use the Moore-Penrose inverse in the case of a close to singular and ill-conditioned, or singular variance-covariance matrix, in the classic Portfolio Selection Problem. In this way the possible singularity of the variance-covariance matrix is tackled in an efficient way so that the various application of the Problem to benefit from the numerical tractability of the Moore-Penro...

The paper presents a new digital image hiding algorithm based on wavelet packets transform and singular value decomposition. The low-frequency sub-band of wavelet packets transform has strong antijamming capacity and the singular value has very strong stability. The presented algorithm implements bit plane decomposition on the secret image and wavelet packet decomposition on the carrier image. ...

This paper discusses an efficient technique for computing filtered matrix-vector (mat-vec) products by exploiting the Lanczos algorithm. The goal of the proposed method, which is the same as that of the truncated singular value decomposition (SVD), is to preserve the quality of the resulting mat-vec product in major singular directions of the matrix. Unlike the SVD-based techniques, the propose...

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.

We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.

The Weyl Horn theorem characterizes a relationship between the eigenvalues and the singular values of an arbitrary matrix Based on that charac terization a fast recursive algorithm is developed to construct numerically a matrix with prescribed eigenvalues and singular values Beside being theoretically interest ing the technique could be employed to create test matrices with desired spectral fea...