In this paper we study diagonal quantum channels and their structure by proving some results giving most applicable instances of them. Firstly, it is shown that action every channel on pure state from computational basis a convex combination states determined transition probabilities. Finally, using the Cholesky decomposition presented an algorithmic method to find explicit form for Kraus opera...

Abstract. Suppose that A ∈ RN×N is symmetric positive semidefinite with rank K ≤ N . Our goal is to decompose A into K rank-one matrices ∑K k=1 gkg T k where the modes {gk} K k=1 are required to be as sparse as possible. In contrast to eigendecomposition, these sparse modes are not required to be orthogonal. Such a problem arises in random field parametrization where A is the covariance functio...

Abstract Spatial statistics often involves Cholesky decomposition of covariance matrices. To ensure scalability to high dimensions, several recent approximations have assumed a sparse factor the precision matrix. We propose hierarchical Vecchia approximation, whose conditional-independence assumptions imply sparsity in factors both and This remarkable property is crucial for applications high-d...

By relating the projective camera model to the perspective one, the intrinsic camera parameters give rise to what is called the calibration matrix. This paper presents two new methods to retrieve the calibration matrix from the projective camera model. In both methods, a collective approach was adopted, using matrix representation. The calibration matrix was retrieved from a quadratic matrix te...

By relating the projective camera model to the perspective one, using homogenous coordinates representation, the interior orientation parameters constitute what is called the calibration matrix. This paper presents two new algorithms to retrieve the calibration matrix from the projective camera model. In both algorithms, a collective approach was adopted, using matrix factorization. The calibra...

Cholesky factorization of large dense matrices is an integral part of many applications in science and engineering. In this paper we report on experiments with different parallel versions of Cholesky factorization on modern high-performance computing architectures. For the parallelization of Cholesky factorization we utilized various standard linear algebra software packages and present perform...

INTRODUCTION The diffusion tensor is a 3x3 positive definite matrix and, therefore, possesses several distinct matrix decompositions, e.g. the Cholesky, and the Eigenvalue decompositions. To date, the Eigenvalue decomposition has been used only in computing tensor-derived quantities [1-4] but not as a parametrization (or equivalently, a representation) in DTI error propagation [5]. Treating a m...

This paper gives perturbation analyses of the Cholesky factorization with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations. The analyses more accurately reflect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of symmetric pivoting usually imp...

Subsurface hydraulic properties are mainly governed by the heterogeneity of the porous medium considered. Our work aims at characterizing the asymptotic dispersion coefficients for highly heterogeneous permeability fields triggered by advection and constant local dispersion-diffusion. We have developed a fully parallel software for simulating flow and transport. We have compared two well-known ...

In this paper we formulate a theory of LU and Cholesky factorization of bi-infinite block Toeplitz matrices A = (Ai−j )i,j∈Zd indexed by i, j ∈ Zd and develop two numerical methods to compute such factorizations. © 2002 Elsevier Science Inc. All rights reserved.