A new inversion-free method for a rational matrix equation

✍ Scribed by Marlliny Monsalve; Marcos Raydan

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 141 KB
• Volume: 433
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2010.02.006

✦ Synopsis

Motivated by the classical Newton-Schulz method for finding the inverse of a nonsingular matrix, we develop a new inversion-free method for obtaining the minimal Hermitian positive definite solution of the matrix rational equation X + A * X -1 A = I, where I is the identity matrix and A is a given nonsingular matrix. We present convergence results and discuss stability properties when the method starts from the available matrix AA * . We also present numerical results to compare our proposal with some previously developed inversion-free techniques for solving the same rational matrix equation.