An algorithm to exactly compute minimal upper bounds in the Loewner order
Finding the smallest matrix that bounds a collection of matrices
Researchers developed an algorithm that can exactly compute the smallest upper bound for any group of matrices—a problem that matters across optimization, quantum computing, and control theory. The method finishes in at most n iterations and works by finding what's called a minimal upper bound in the Loewner order, a mathematical framework for comparing matrices.
Many optimization and engineering problems require finding a single matrix that bounds multiple others, but unlike ordering regular numbers, matrices often have no unique smallest upper bound. This algorithm provides a guaranteed way to find one, enabling faster and more precise solutions in quantum information processing, control systems design, and numerical computations that rely on comparing matrices in this specific way.