Arnoldi Iteration

Arnoldi iteration is a mathematical process used to find approximate eigenvalues and eigenvectors of large matrices, which are important in understanding systems like vibrations or stability. It works by starting with a vector and repeatedly applying the matrix, then orthogonalizing each new vector to build an orthonormal basis for a smaller subspace. This reduces complex problems into simpler ones, enabling efficient calculations of key properties without handling the full matrix. Essentially, Arnoldi iteration transforms a large, complex problem into a manageable form while preserving essential information about its behavior.