SOLVING MATRIX POLYNOMIALS BY NEWTON'S METHOD WITH EXACT LINE SEARCHES
Jong Hyeon Seo, Hyun‐Min Kim · Journal of the Korea Society for Industrial and Applied Mathematics · 2008
One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the formP(X) = A0X m +A1X mi1 +¢¢¢+Am, whereA0;A1;¢¢¢ ;Am and X are n £ n complex matrices. Newton's method was introduced a useful tool for solv- ing the equation P(X) = 0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.