Solution of quadratic matrix equations by least-squares method
Charles C. Lee, H. P. Niu · Quarterly of Applied Mathematics · 1972
A least-square method is described for obtaining the solutions A A and B B for the matrix equations Y 2 − Y D + S = 0 {Y^2} - YD + S = 0 and Y 2 − D Y + S = 0 {Y^2} - DY + S = 0 respectively. No limitation is set on A A , B B , D D , and S S except that they be square matrices. An illustrated example, including computing procedures, is discussed. The mathematical solutions presented should prove useful for solving the eigenvalue problem ( λ 2 I + λ D + S ) X = 0 \left ( {{\lambda ^2}I + \lambda D + S} \right )X = 0 , especially when the dimension of the matrices is large.