Related papers: AMPS: An Augmented Matrix Formulation for Principa…

Subset selection from massive data with noised information is increasingly popular for various applications. This problem is still highly challenging as current methods are generally slow in speed and sensitive to outliers. To address the…

We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…

Augmented Large Language Models (LLMs) enhance the capabilities of standalone LLMs by integrating external data sources through API calls. In interactive LLM applications, efficient scheduling is crucial for maintaining low request…

We present a novel framework, namely AADMM, for acceleration of linearized alternating direction method of multipliers (ADMM). The basic idea of AADMM is to incorporate a multi-step acceleration scheme into linearized ADMM. We demonstrate…

As an extension of the alternating direction method of multipliers (ADMM), the semi-proximal ADMM (sPADMM) has been widely used in various fields due to its flexibility and robustness. In this paper, we first show that the two-block sPADMM…

We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…

A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic-solids. The AMP scheme remains stable and second-order accurate even…

In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…

This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…

Transformers are at the core of modern AI nowadays. They rely heavily on matrix multiplication and require efficient acceleration due to their substantial memory and computational requirements. Quantization plays a vital role in reducing…

We introduce a new algorithm and software for solving linear equations in symmetric diagonally dominant matrices with non-positive off-diagonal entries (SDDM matrices), including Laplacian matrices. We use pre-conditioned conjugate gradient…

Prompt engineering is very important to enhance the performance of large language models (LLMs). When dealing with complex issues, prompt engineers tend to distill multiple patterns from examples and inject relevant solutions to optimize…

In this paper we present an adaptable fast matrix multiplication (AFMM) algorithm, for two nxn dense matrices which computes the product matrix with average complexity Tavg(n) = d1d2n3 with the acknowledgement that the average count is…

The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…

This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…

We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…

Approximate full mass matrix methods for the material point method, known as FMPM(k) of order k, can improve the calculation of grid velocities from grid momentum. It can be implemented in any MPM code by inserting a new calculation task…

Optimization models with decision variables in multiple time scales are widely used across various fields such as integrated planning and scheduling. To address scalability challenges in these models, we present the Parametric Autotuning…

The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aiming at the simulation of large but finite-size photonic…

We present a Kokkos-accelerated implementation of the Moment Tensor Potential (MTP) for LAMMPS, designed to improve both computational performance and portability across CPUs and GPUs. This package introduces an optimized CPU…