Rational matrix approximation

Rational matrix approximation involves representing a complex matrix function with a simpler one composed of ratios of polynomial functions—called rational functions. This process is used to simplify calculations or analysis by approximating the original matrix with a more manageable form while preserving key properties. Essentially, it finds a “close enough” version of the matrix that is easier to work with mathematically, enabling efficient algorithms in applications like control systems, signal processing, and numerical simulations. The goal is to balance accuracy with computational simplicity, making complex matrix functions more accessible for analysis and implementation.