Related papers: Low-rank and sparse approximations for contact mec…

Large language models (LLM) have achieved remarkable performance across a wide range of tasks. However, their substantial parameter sizes pose significant challenges for deployment on edge devices with limited computational and memory…

There is growing awareness that errors in the model equations cannot be ignored in data assimilation methods such as four-dimensional variational assimilation (4D-Var). If allowed for, more information can be extracted from observations,…

Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…

The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…

The ability to reason about and predict the outcome of contacts is paramount to the successful execution of many robot tasks. Analytical rigid-body contact models are used extensively in planning and control due to their computational…

High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…

An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…

We consider the problem of optimal sparse output feedback controller synthesis for continuous linear time invariant systems when the feedback gain is static and subject to specified structural constraints. Introducing an additional term…

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose…

We present a contact mechanics problem, which we consider to be representative for contacts between nominally flat surfaces. The main ingredients of the mathematically fully defined contact problem are: Self-affine roughness, linear…

Many applications of machine learning involve the analysis of large data frames-matrices collecting heterogeneous measurements (binary, numerical, counts, etc.) across samples-with missing values. Low-rank models, as studied by Udell et al.…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Active and passive thermography are two efficient techniques extensively used to measure heterogeneous thermal patterns leading to subsurface defects for diagnostic evaluations. This study conducts a comparative analysis on low-rank matrix…

Non-prehensile manipulation such as pushing is typically subject to uncertain, non-smooth dynamics. However, modeling the uncertainty of the dynamics typically results in intractable belief dynamics, making data-efficient planning under…

Large Language Models (LLMs) have demonstrated remarkable proficiency in language comprehension and generation; however, their widespread adoption is constrained by substantial bandwidth and computational demands. While pruning and low-rank…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

This paper is concerned with the development and analysis of an iterative solver for high-dimensional second-order elliptic problems based on subspace-based low-rank tensor formats. Both the subspaces giving rise to low-rank approximations…