condition number
- Europe > United Kingdom (0.14)
- Asia > China > Hong Kong (0.04)
- North America > United States > New Jersey > Middlesex County > Piscataway (0.04)
- Europe > Switzerland > Zürich > Zürich (0.14)
- North America > United States > Washington (0.04)
- Europe > Spain > Galicia > Madrid (0.04)
- Asia > Middle East > Jordan (0.04)
- Research Report > Experimental Study (1.00)
- Research Report > New Finding (0.67)
- Research Report > Experimental Study (0.93)
- Research Report > New Finding (0.92)
- Information Technology > Artificial Intelligence > Vision (1.00)
- Information Technology > Artificial Intelligence > Machine Learning > Neural Networks > Deep Learning (1.00)
- Information Technology > Artificial Intelligence > Natural Language > Large Language Model (0.94)
- Information Technology > Artificial Intelligence > Representation & Reasoning > Optimization (0.92)
- Europe > Italy > Abruzzo > L'Aquila Province > L'Aquila (0.04)
- Europe > Austria > Tyrol > Innsbruck (0.04)
- Asia > Middle East > Jordan (0.04)
- Europe > United Kingdom > England > Cambridgeshire > Cambridge (0.04)
- North America > Canada > Ontario > Toronto (0.14)
- North America > United States > California > Santa Clara County > Sunnyvale (0.04)
Block Broyden's Methods for Solving Nonlinear Equations
This paper studies quasi-Newton methods for solving nonlinear equations. We propose block variants of both good and bad Broyden's methods, which enjoy explicit local superlinear convergence rates. Our block good Broyden's method has a faster condition-number-free convergence rate than existing Broyden's methods because it takes the advantage of multiple rank modification on Jacobian estimator. On the other hand, our block bad Broyden's method directly estimates the inverse of the Jacobian provably, which reduces the computational cost of the iteration. Our theoretical results provide some new insights on why good Broyden's method outperforms bad Broyden's method in most of the cases. The empirical results also demonstrate the superiority of our methods and validate our theoretical analysis.
- Asia > China > Shanghai > Shanghai (0.04)
- Asia > China > Hong Kong (0.04)
- North America > United States (0.04)
- Asia > Middle East > Republic of Türkiye (0.04)
- Asia > China > Shanghai > Shanghai (0.04)
- Asia > China > Hong Kong (0.04)
- North America > United States (0.04)
- Asia > Middle East > Republic of Türkiye (0.04)
- North America > United States > California > Alameda County > Berkeley (0.05)
- Asia > Middle East > Jordan (0.04)
- North America > Canada > Quebec > Montreal (0.04)
- Asia > China (0.04)
- Asia > China > Jiangsu Province > Nanjing (0.04)
- North America > United States > North Carolina (0.04)
- North America > Canada > Quebec > Montreal (0.04)
- (3 more...)