相关论文: Differential equations for real-structured (and un…

This paper presents a new distance geometry algorithm for calculating atomic coordinates from estimates of the interatomic distances, which maintains the positions of the atoms in a known rigid substructure. Given an $M \times 3$ matrix of…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

This paper deals with the reconstruction of a discrete measure $\gamma_Z$ on $\mathbb{R}^d$ from the knowledge of its pushforward measures $P_i\#\gamma_Z$ by linear applications $P_i: \mathbb{R}^d \rightarrow \mathbb{R}^{d_i}$ (for instance…

The distance matrix of a dataset $X$ of $n$ points with respect to a distance function $f$ represents all pairwise distances between points in $X$ induced by $f$. Due to their wide applicability, distance matrices and related families of…

The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more…

With the emergence of Artificial Intelligence, numerical algorithms are moving towards more approximate approaches. For methods such as PCA or diffusion maps, it is necessary to compute eigenvalues of a large matrix, which may also be dense…

Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

A Euclidean distance matrix $D(\alpha)$ is defined by $D_{ij}=(\alpha_i-\alpha_j)^2$, where $\alpha=(\alpha_1,\ldots,\alpha_n)$ is a real vector. We prove that $D(\alpha)$ cannot be written as a sum of $\left[2\sqrt{n}-2\right]$ nonnegative…

Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…

We study the differential structure of the set of real logarithms of a non-singular real matrix, under the assumption that the matrix is either semi-simple or orthogonal.

A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…

We consider the problem of finding nonzero eigenvalues and the corresponding eigenvectors of a matrix $AA^{\top}$, where $A$ is a special incidence matrix; This matrix can equivalently be defined based on a match relation between some…

A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…

Consider an $n\times n$ matrix polynomial $P(\lambda)$ and a set $\Sigma$ consisting of $k \le n$ distinct complex numbers. In this paper, a (weighted) spectral norm distance from $P(\lambda)$ to the matrix polynomials whose spectra include…

We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the…

We present an algorithm to compute the Jordan chain of a nearly defective matrix with a $2\times2$ Jordan block. The algorithm is based on an inverse-iteration procedure and only needs information about the invariant subspace corresponding…

This paper is on the normal approximation of singular subspaces when the noise matrix has i.i.d. entries. Our contributions are three-fold. First, we derive an explicit representation formula of the empirical spectral projectors. The…

The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound.…