Research Article
Effective Algorithms for Solving Trace Minimization Problem in Multivariate Statistics
Algorithm 1
Riemannian Newton’s method for Problem
1.
(1)  Choose an initial point .  (2)  fordo  (3)  Compute that satisfies and .  (4)  Compute the partition matrix by Lemma 4 and the vector by (68). Compute that satisfies the symmetric linear equation (69).  (5)  Partition as , where .  (6)  Construct and that satisfy and .  (7)  Compute .  (8)  Compute the next iterate , where is a retraction on .  (9)  end for 
