Related papers: hm-toolbox: Matlab software for HODLR and HSS matr…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
A simple MATLAB implementation of hierarchical shape functions on 2D rectangles is explained and available for download. Global shape functions are ordered for a given polynomial degree according to the indices of the nodes, edges, or…
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…
For an easy use of model order reduction techniques in applications, software solutions are needed. In this paper, we describe the MORLAB, Model Order Reduction LABoratory, toolbox as an efficient implementation of model reduction…
Bridging the gap between algorithm development and hardware realization remains a persistent challenge, particularly in latency- and resource-constrained domains such as wireless communication. While MATLAB provides a mature environment for…
Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper…
Recent advances in code generation have illuminated the potential of employing large language models (LLMs) for general-purpose programming languages such as Python and C++, opening new opportunities for automating software development and…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
Factorization machines (FMs) are a supervised learning approach that can use second-order feature combinations even when the data is very high-dimensional. Unfortunately, despite increasing interest in FMs, there exists to date no efficient…
We consider the discretization of time-space diffusion equations with fractional derivatives in space and either 1D or 2D spatial domains. The use of implicit Euler scheme in time and finite differences or finite elements in space, leads to…
TMAC is a toolbox written in C++11 that implements algorithms based on a set of modern methods for large-scale optimization. It covers a variety of optimization problems, which can be both smooth and nonsmooth, convex and nonconvex, as well…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
Recent advancements in function calling and tool use have significantly enhanced the capabilities of large language models (LLMs) by enabling them to interact with external information sources and execute complex tasks. However, the limited…
Artificial intelligence (AI) application domains consist of a mix of tensor operations with high and low arithmetic intensities (aka reuse). Hierarchical (i.e. compute along multiple levels of memory hierarchy) and heterogeneous (multiple…
The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
HTM-MAT is a MATLAB based toolbox for implementing cortical learning algorithms (CLA) including related cortical-like algorithms that possesses spatiotemporal properties. CLA is a suite of predictive machine learning algorithms developed by…
In this work we introduce a new multiscale artificial neural network based on the structure of $\mathcal{H}$-matrices. This network generalizes the latter to the nonlinear case by introducing a local deep neural network at each spatial…
In software engineering, the meticulous configuration of software tools is crucial in ensuring optimal performance within intricate systems. However, the complexity inherent in selecting optimal configurations is exacerbated by the…