Lanczos Algorithm

The Lanczos Algorithm is a computational method used to efficiently find important features, like eigenvalues and eigenvectors, of large matrices—mathematical structures representing complex data or systems. It works by transforming the large matrix into a smaller, simpler form called a tridiagonal matrix, preserving key properties. This simplification allows for faster calculations and insights into the system’s behavior without processing the entire large matrix. The algorithm is widely used in physics, engineering, and data science, especially where dealing with big, complex datasets or systems makes direct analysis computationally impractical.