Efficient computation of the extreme solutions of ๐+๐ด*๐โปยน๐ด=๐ and ๐-๐ด*๐โปยน๐ด=๐
Beatrice Meini ยท Mathematics of Computation ยท 2001
We propose a new quadratically convergent algorithm, having a low computational cost per step and good numerical stability properties, which allows the simultaneous approximation of the extreme solutions of the matrix equations X + A โ X โ 1 A = Q X+A^* X^{-1}A=Q and X โ A โ X โ 1 A = Q X-A^*X^{-1}A=Q . The algorithm is based on the cyclic reduction method.