DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

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This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

In this thesis we will present and analyze randomized algorithms for numerical linear algebra problems. An important theme in this thesis is randomized low-rank approximation. In particular, we will study randomized low-rank approximation of matrix functio ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

The increasing complexity of transformer models in artificial intelligence expands their computational costs, memory usage, and energy consumption. Hardware acceleration tackles the ensuing challenges by designing processors and accelerators tailored for t ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...

Genes implicated in translation control have been associated with autism spectrum disorders (ASDs). However, some important genetic causes of autism, including the 16p11.2 microdeletion, bear no obvious connection to translation. Here, we use proteomics, g ...

The rapid progress in machine learning in recent years has been based on a highly productive connection to gradient-based optimization. Further progress hinges in part on a shift in focus from pattern recognition to decision-making and multi-agent problems ...

Two -particle Bose-Einstein momentum correlation functions are studied for charged-hadron pairs in lead -lead collisions at a center -of -mass energy per nucleon pair of .'/sNN = 5.02 TeV. The data sample, containing 4.27 x 109 minimum bias events correspo ...

The desire and ability to place AI-enabled applications on the edge has grown significantly in recent years. However, the compute-, area-, and power-constrained nature of edge devices are stressed by the needs of the AI-enabled applications, due to a gener ...

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

Multiple tensor-times-matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine ...

Given a family of nearly commuting symmetric matrices, we consider the task of computing an orthogonal matrix that nearly diagonalizes every matrix in the family. In this paper, we propose and analyze randomized joint diagonalization (RJD) for performing t ...

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

The need for high-quality automated seizure detection algorithms based on electroencephalography (EEG) becomes ever more pressing with the increasing use of ambulatory and long-term EEG monitoring. Heterogeneity in validation methods of these algorithms in ...

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they now arise in an increasingly large number of applications. In this work, we consider algebraic parame ...

State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

A new model is proposed for the consolidation of hybrid textiles, in which air entrapment and dissolution are considered. One of the key parameters is tow permeability, which is described by the analytical model of Gebart and validated at very high fibre v ...

Rectified-linear-unit (ReLU) neural networks, which play a prominent role in deep learning, generate continuous and piecewise-linear (CPWL) functions. While they provide a powerful parametric representation, the mapping between the parameter and function s ...

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

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SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Randomized low-rank approximation and its applications

Randomized flexible GMRES with deflated restarting

Accelerator-driven Data Arrangement to Minimize Transformers Run-time on Multi-core Architectures

Spectral Estimators for High-Dimensional Matrix Inference

The Power of Two Matrices in Spectral Algorithms for Community Recovery

The autism susceptibility kinase, TAOK2, phosphorylates eEF2 and modulates translation

A gentle introduction to gradient-based optimization and variational inequalities for machine learning

Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at √sNN=5.02 TeV

Exploring High-Performance and Energy-Efficient Architectures for Edge AI-Enabled Applications

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

COMMUNICATION LOWER BOUNDS AND OPTIMAL ALGORITHMS FOR MULTIPLE TENSOR-TIMES-MATRIX COMPUTATION

RANDOMIZED JOINT DIAGONALIZATION OF SYMMETRIC

Scalable constrained optimization

SzCORE: Seizure Community Open-Source Research Evaluation framework for the validation of electroencephalography-based automated seizure detection algorithms

Preconditioning techniques for generalized Sylvester matrix equations

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

A model for the consolidation of hybrid textiles considering air entrapment, dissolution and diffusion

Stable parameterization of continuous and piecewise-linear functions