Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches
Nicholas John Higham, Hyun‐Min Kim · SIAM Journal on Matrix Analysis and Applications · 2001
We show how to incorporate exact line searches into Newton's method for solving the quadratic matrix equation AX 2 + BX + C = 0, where A, B and C are square matrices. The line searches are relatively inexpensive and improve the global convergence properties of Newton's method in theory and in practice. We also derive a condition number for the problem and show how to compute the backward error of an approximate solution.