Block Broyden's Methods for Solving Nonlinear Equations
Authors: Chengchang Liu, Cheng Chen, Luo Luo, John C.S. Lui
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The empirical results also demonstrate the superiority of our methods and validate our theoretical analysis. Our experiments are conducted on a PC with Apple M1 and all algorithms are implemented in Python 3.8.12. |
| Researcher Affiliation | Academia | Chengchang Liu Department of Computer Science & Engineering The Chinese University of Hong Kong 7liuchengchang@gmail.com Cheng Chen Shanghai Key Laboratory of Trustworthy Computing East China Normal University chchen@sei.ecnu.edu.cn Luo Luo School of Data Science Fudan University luoluo@fudan.edu.cn John C.S. Lui Department of Computer Science & Engineering The Chinese University of Hong Kong cslui@cse.cuhk.edu.hk |
| Pseudocode | Yes | Algorithm 1 Block Good Broyden s Method (BGB) Algorithm 2 Block Bad Broyden s Method (BBB) |
| Open Source Code | No | The paper does not contain any explicit statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper states, "We validate our methods on the Chandrasekhar H-equation which is well studied in the previous literature [25, 29, 50]". This refers to a mathematical problem, not a publicly available dataset with a specific link or formal citation for data files. |
| Dataset Splits | No | The paper does not provide specific percentages or counts for training, validation, or test dataset splits. It describes the Chandrasekhar H-equation problem and how parameters were set for simulations. |
| Hardware Specification | Yes | Our experiments are conducted on a PC with Apple M1 and all algorithms are implemented in Python 3.8.12. |
| Software Dependencies | No | The paper states, "all algorithms are implemented in Python 3.8.12." While Python version is given, no other specific software dependencies or libraries with their version numbers are listed, which is required for reproducibility. |
| Experiment Setup | Yes | We set c = 1 − 10^−12 for the H-equation and choose the block size k = N/10 for the proposed methods. In all cases, we use the same inputs B0 = 0.1IN (H0 = 10IN) for all algorithms. By fixing N = 400 and setting c = {1 − 10^−1, 1 − 10^−3, 1 − 10^−5}, we obtain different condition numbers of (21) as κ = 2, 31, 327. For each κ, we also vary the block size k = {1, 10, 100} for BGB and BBB algorithms. |