Chemistry, mathematics and physics are central to our understanding of nature. Physics explores the fundamental laws of mechanics, electromagnetism, quantum mechanics and relativity. Chemistry studies ...

Abstract: This article proposes a novel hardware-efficient QR algorithm and its VLSI architecture to compute the eigenvalue decomposition (EVD) of symmetric matrices. By replacing the computationally ...

Implementation of the Bathe Subspace Iteration algorithms from the textbook Finite Element Procedures (1996), Table 11.3. A couple of twists have been added, which seem to improve convergence. This ...

Spectral clustering is quite complex, but it can reveal patterns in data that aren't revealed by other clustering techniques. Data clustering is the process of grouping data items so that similar ...

This paper concerns the more foundational tasks of distributed dense linear algebra. While a single TPU core can already store and operate on large matrices (e.g., of size 16,384, 32,768 in single ...

where M is an nxn-matrix depending on a parameter. This package aims to provide state-of-the-art algorithms to solve this problem, as well as a framework to formulate applications and easy access to ...

Algorithms are pre-defined, self-contained sets of instructions designed to execute diverse functions, and they have been around for longer than you might expect. From ancient Babylon to the present ...

Automatic differentiation (AD) is a powerful tool that allows calculating derivatives of implemented algorithms with respect to all of their parameters up to machine precision, without the need to ...

The past decade has been marked with a proliferation of community detection algorithms that aim to organize nodes (e.g., individuals, brain regions, variables) into modular structures that indicate ...