Chebyshev Davidson Algorithm

The Chebyshev-Davidson algorithm and related Chebyshev polynomial-based methods are used to efficiently solve eigenvalue problems and approximate complex functions, particularly in high-dimensional spaces. Current research focuses on applying these techniques within various machine learning architectures, including neural networks and Bayesian models, as well as in other areas like state estimation and signal processing, often leveraging the polynomials' approximation properties for improved accuracy and efficiency. This work is significant because it addresses computational bottlenecks in diverse fields, enabling faster and more accurate solutions to challenging problems in areas ranging from quantum Hamiltonian learning to image analysis and robotics.