A new upper bound for the growth factor in Gaussian elimination with complete pivoting
Year: 2025
Type: article
Abstract: The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of .
DOI: 10.1112/blms.70034
Authors: Ankit Bisain, Alan Edelman, John Urschel
Institution: Massachusetts Institute of Technology
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,930
Funders: National Science Foundation, U.S. Department of Energy, United States Agency for International Development, University of Pennsylvania, Pennsylvania State University, Equinor, Norges Forskningsråd, Advanced Research Projects Agency - Energy, Advanced Research Projects Agency, Division of Electrical, Communications and Cyber Systems
Awards: G1467515376, G1498456215, G2360264995, SWIFT: LARGE: Adaptive Radio Frequency Interference Cancellation for Radio Science Observatories, G4536555042, G620536356, G6553639979, Collaborative Research: Frameworks: Convergence of Bayesian inverse methods and scientific machine learning in Earth system models through universal differentiable programming, G7146022962, Framework: Software: Next-Generation Cyberinfrastructure for Large-Scale Computer-Based Scientific Analysis and Discovery, G7789225813, THIS COOPERATIVE AGREEMENT IS AWARDED TO CARNEGIE MELLON UNIVERSITY FOR A PROJECT ENTITLED “HIGH-FIDELITY ACCELERATED DESIGN OF HIGH-PERFORMANCE ELECTROCHEMICAL SYSTEMS”. THIS AWARD IS BEING MADE IN ACCORDANCE WITH FOA NUMBER DE-FOA-0002107 DIFFERENTIATE AND APPLICATION CONTROL NUMBER 2107-1548., ACCELERATING COUPLED HVAC BUILDING SIMULATION WITH A NEURAL COMPONENT ARCHITECTURE
OpenAlex ID: W4407953220