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We propose a homogeneous primal-dual interior-point method to solve sum-of-squares optimization problems by combining non-symmetric conic optimization techniques and polynomial interpolation. The approach optimizes directly over the…

Optimization and Control · Mathematics 2018-12-24 Dávid Papp , Sercan Yıldız

Large language models (LLMs) have transformed natural language processing but face critical deployment challenges in device-edge systems due to resource limitations and communication overhead. To address these issues, collaborative…

Signal Processing · Electrical Eng. & Systems 2025-07-18 Jiahong Ning , Ce Zheng , Tingting Yang

General sparse matrix-matrix multiplication (SpGEMM) is a fundamental building block for numerous applications such as algebraic multigrid method (AMG), breadth first search and shortest path problem. Compared to other sparse BLAS routines,…

Mathematical Software · Computer Science 2015-09-15 Weifeng Liu , Brian Vinter

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

Machine Learning · Statistics 2015-11-24 Zhanxing Zhu , Amos J. Storkey

Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning…

Numerical Analysis · Mathematics 2025-12-25 Zexi Fan , Yan Sun , Shihao Yang , Yiping Lu

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

Numerical Analysis · Mathematics 2025-02-13 Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…

Numerical Analysis · Mathematics 2015-05-05 Diego Galindo , Peter Jantsch , Clayton G. Webster , Guannan Zhang

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…

Computational Physics · Physics 2020-07-15 M. Paul Laiu , Zheng Chen , Cory D. Hauck

We consider a sparse matrix-matrix multiplication (SpGEMM) setting where one matrix is square and the other is tall and skinny. This special variant, called TS-SpGEMM, has important applications in multi-source breadth-first search,…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-08-23 Isuru Ranawaka , Md Taufique Hussain , Charles Block , Gerasimos Gerogiannis , Josep Torrellas , Ariful Azad

We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive semidefinite (PSD) constraints. In contrast to previous…

Optimization and Control · Mathematics 2020-08-07 Yang Zheng , Giovanni Fantuzzi , Antonis Papachristodoulou , Paul Goulart , Andrew Wynn

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…

Numerical Analysis · Mathematics 2023-10-19 Yan Cheng , Xi Yang

The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in many numerical schemes and its performance is known to be severely limited by main memory access. Several numerical schemes require the multiplication of…

Numerical Analysis · Mathematics 2023-01-11 Christie L. Alappat , Georg Hager , Olaf Schenk , Gerhard Wellein

Even distribution of irregular workload to processing units is crucial for efficient parallelization in many applications. In this work, we are concerned with a spatial partitioning called rectilinear partitioning (also known as generalized…

Data Structures and Algorithms · Computer Science 2020-09-17 Abdurrahman Yaşar , Muhammed Fatih Balin , Xiaojing An , Kaan Sancak , Ümit V. Çatalyürek

Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…

Optimization and Control · Mathematics 2021-03-26 Alp Yurtsever , Joel A. Tropp , Olivier Fercoq , Madeleine Udell , Volkan Cevher

Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and…

Numerical Analysis · Mathematics 2024-08-23 Yutian Tao , Eftychios Sifakis

We present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination, and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which…

Mathematical Software · Computer Science 2015-02-27 Pieter Ghysels , Xiaoye S. Li , Francois-Henry Rouet , Samuel Williams , Artem Napov

The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…

Numerical Analysis · Mathematics 2021-08-31 Abal-Kassim Cheik Ahamed , Frédéric Magoulès

Sparse Matrix Vector multiplication (SpMV) is one of basic building blocks in scientific computing, and acceleration of SpMV has been continuously required. In this research, we aim for accelerating SpMV on recent CPUs for sparse matrices…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-05-12 Takeshi Fukaya , Koki Ishida , Akie Miura , Takeshi Iwashita , Hiroshi Nakashima

We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including…

Data Structures and Algorithms · Computer Science 2023-10-30 Arun Jambulapati , Jerry Li , Christopher Musco , Kirankumar Shiragur , Aaron Sidford , Kevin Tian

In recent years, novel AI accelerators have emerged as promising alternatives to GPU for AI model training and inference tasks. One such accelerator, the Cerebras CS-3, achieves strong performance on large model training as well as…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-01 Milan Shah , Sheng Di , Michela Becchi