Related papers: The Multi-Symplectic Lanczos Algorithm and Its App…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
In this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs (MIMO). This approach is based on the projection of the initial problem onto…
We investigate the solution of low-rank matrix approximation problems using the truncated SVD. For this purpose, we develop and optimize GPU implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work…
Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…
Supervised deep learning approaches can artificially increase the resolution of microscopy images by learning a mapping between two image resolutions or modalities. However, such methods often require a large set of hard-to-get…
We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved…
Positive semi-definite matrices commonly occur as normal matrices of least squares problems in statistics or as kernel matrices in machine learning and approximation theory. They are typically large and dense. Thus algorithms to solve…
Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…
We propose inexact subspace iteration for solving high-dimensional eigenvalue problems with low-rank structure. Inexactness stems from low-rank compression, enabling efficient representation of high-dimensional vectors in a low-rank tensor…
The Levenberg-Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies LM parameter updates have been made tractable for highly parameterized…
The problem of approximating a matrix by a low-rank one has been extensively studied. This problem assumes, however, that the whole matrix has a low-rank structure. This assumption is often false for real-world matrices. We consider the…
This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that…
Despite its exceptional soft tissue contrast, Magnetic Resonance Imaging (MRI) faces the challenge of long scanning times compared to other modalities like X-ray radiography. Shortening scanning times is crucial in clinical settings, as it…
We consider the approximation of $B^T (A+sI)^{-1} B$ where $A\in\mathbb{R}^{n\times n}$ is large, symmetric positive definite, and has a dense spectrum, and $B\in\mathbb{R}^{n\times p}$, $p\ll n$. Our target application is the computation…
Lanczos methods for solving $\textit{A}\textbf{x}=\textbf{b}$ consist in constructing a sequence of vectors $(\textbf{x}_k), k=1,...$ such that $\textbf{r}_{k}=\textbf{b}-\textit{A}\textbf{x}_{k}=\textit{P}_{k}(\textit{A})\textbf{r}_{0}$,,…
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale…
Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or block Lanczos-type solvers often exhibit large oscillations in the residual norms…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Multitask learning, i.e. taking advantage of the relatedness of individual tasks in order to improve performance on all of them, is a core challenge in the field of machine learning. We focus on matrix regression tasks where the rank of the…
We consider the following constrained Rayleigh quotient optimization problem (CRQopt) $$ \min_{x\in \mathbb{R}^n} x^{T}Ax\,\,\mbox{subject to}\,\, x^{T}x=1\,\mbox{and}\,C^{T}x=b, $$ where $A$ is an $n\times n$ real symmetric matrix and $C$…