An Inversion-Free Method For Computation Of The Square Roots Of Real Matrices

An efficient method for computation of the square roots of real matrices is developed. Our method is based on the Adomian decomposition method and obviates the use of any matrix inversion as a significant advantage. Additionally, our method does not require any matrix factorization and only instead relies on the simple operations of addition and multiplication. We demonstrate the rapid convergence of our new approach in several numerical examples. Also, CPU-time analyses incorporating random matrices of large dimensions (n = 10, 000) shows the superiority of the proposed method over the previous Newton-type algorithms.