Related papers: SuperDC: Stable superfast divide-and-conquer eigen…

The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…

This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…

Training stability is a persistent challenge in the pre-training of large language models (LLMs), particularly for architectures such as Post-Norm Transformers, which are prone to gradient explosion and dissipation. In this paper, we…

We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy…

This paper presents a self-contained factorization for the delay Vandermonde matrix (DVM), which is the super class of the discrete Fourier transform, using sparse and companion matrices. An efficient DVM algorithm is proposed to reduce the…

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of…

This paper develops a new storage-optimal algorithm that provably solves generic semidefinite programs (SDPs) in standard form. This method is particularly effective for weakly constrained SDPs. The key idea is to formulate an approximate…

We consider the problem of developing interpretable and computationally efficient matrix decomposition methods for matrices whose entries have bounded support. Such matrices are found in large-scale DNA methylation studies and many other…

Solving Markov Decision Processes (MDPs) remains a central challenge in sequential decision-making, especially when dealing with large state spaces and long-term optimization criteria. A key step in Bellman dynamic programming algorithms is…

This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field $f$ defined on a $d$-dimensional simplicial complex $K$, with $d \leq 3$. Our work revisits the seminal algorithm…

We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate…

In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid…

Large models and enormous data are essential driving forces of the unprecedented successes achieved by modern algorithms, especially in scientific computing and machine learning. Nevertheless, the growing dimensionality and model…

Sequential Monte Carlo (SMC) methods offer a principled approach to Bayesian uncertainty quantification but are traditionally limited by the need for full-batch gradient evaluations. We introduce a scalable variant by incorporating…

Homomorphic permutation is fundamental to privacy-preserving computations based on batch-encoding homomorphic encryption. It underpins nearly all homomorphic matrix operations and predominantly influences their complexity. Permutation…

In this paper, we present a generalized Cuppen's divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. We extend the Cuppen's work to the rank two modifications of the form $A =T +\beta_1\bw_1\bw_1^T +…

This paper considers master equations for Markovian kinetic schemes that possess the detailed balance property. Chemical kinetics, as a prime example, often yields large-scale, highly stiff equations. Based on chemical intuitions, Sumiya et…

We present two improvements to our previous dynamical overlap HMC algorithm. We introduce a new method of differentiating the eigenvectors of the Kernel operator, which removes an instability in the fermionic force. Secondly, by simulating…

Recent results on supercomputers show that beyond 65K cores, the efficiency of molecular dynamics simulations of interfacial systems decreases significantly. In this paper, we introduce a dynamic cutoff method (DCM) for interfacial systems…