Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Fast methods for estimating the Numerical rank of large matrices
Authors: Shashanka Ubaru, Yousef Saad
ICML 2016 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section, we illustrate the performance of the rank estimation techniques on matrices from various typical applications. In the first experiment, we use a 5, 981 5, 981 matrix named ukerbe1 from the AG-Monien group (the matrix is a Laplacian of an undirected graph), available in the University of Florida Sparse Matrix Collection (Davis & Hu, 2011) database. The performances of the Chebyshev Polynomial filter method and the extended Mc Weeny filter method for estimating the numerical rank of this matrix2 are shown in figure 3. |
| Researcher Affiliation | Academia | Shashanka Ubaru EMAIL Yousef Saad EMAIL Department of Computer Science and Engineering, University of Minnesota, Twin Cities, MN USA |
| Pseudocode | Yes | Algorithm 1 describes our approach for estimating the approximate rank rε by the two polynomial filtering methods discussed earlier. |
| Open Source Code | Yes | Matlab codes are available at http://www-users.cs. umn.edu/ ubaru/codes/rank_estimation.zip |
| Open Datasets | Yes | In the first experiment, we use a 5, 981 5, 981 matrix named ukerbe1 from the AG-Monien group (the matrix is a Laplacian of an undirected graph), available in the University of Florida Sparse Matrix Collection (Davis & Hu, 2011) database. |
| Dataset Splits | No | No explicit train/test/validation splits are mentioned for the datasets used in the experiments. The paper uses existing matrices from databases or image datasets for evaluation. |
| Hardware Specification | Yes | The estimation of its rank by the Chebyshev filter method took only 7.18 secs on average (over 10 trials) on a standard 3.3GHz Intel-i5 machine. |
| Software Dependencies | No | No specific software versions are mentioned. The paper only states 'Matlab codes are available...'. |
| Experiment Setup | No | No specific experimental setup details such as hyperparameters, learning rates, or optimizer settings are provided. The paper describes the general methods and their application to matrices. |