Practical Approaches to Approximate Dominant Eigenvalues in Large Matrices

In numerous machine learning algorithms, the computation of eigenvectors and eigenvalues plays a pivotal role in optimizing models. Depending on the specific use case, it is frequently adequate to compute only a subset of dominant eigenvectors or utilize estimations. Handling this task for large matrices poses a challenge, as standard machine learning packages often lack suitable implementations. We explores various techniques for approximating dominant eigenvectors in the context of potentially large symmetric, real-valued matrices and offer an overview of established methods, analyzing their potentials and limitations, including implementation details.