$AB$-algorithm and its application for solving matrix square roots
Provides a new theoretical framework for computing matrix square roots, but the practical impact is unclear as no benchmarks or comparisons are given.
Proposed an accelerated iterative method for computing stable subspaces of regular matrix pencils, achieving convergence to matrix square roots (both nonsingular and singular) with any desired order.
This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a discrete-type flow depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order.