This paper presents a novel approach for determining the polar decomposition of a complex (real) matrix, accompanied by a thorough examination of its convergence. The proposed class of methods' structure is inspired by Petkovic's idea for computing the Moore-Penrose inverse of a matrix A using polynomials. This class of methods, rooted in matrix multiplications, circumvents the need for matrix inversion. Several categories of methods with varying convergence orders are introduced and scrutinized. The efficacy of these proposed methods is demonstrated through numerical experiments, comparing them with alternative approaches. The study focuses on random matrices of dimensions $n\times n$, where $n$ takes values of $80$, $100$, $120$, $150$, $180$, and $200$ and several ill-conditioned matrices. The assessment includes key metrics such as the average number of iterations, matrix multiplications, and execution time for each method under consideration. The results affirm the efficiency of certain proposed methods in comparison to others.
Sheikhi, S. and Esmaeili, H. (2026). A class of inversion-free iterative methods to find polar decomposition. Journal of Mathematical Modeling, (), -. doi: 10.22124/jmm.2026.32920.2996
MLA
Sheikhi, S. , and Esmaeili, H. . "A class of inversion-free iterative methods to find polar decomposition", Journal of Mathematical Modeling, , , 2026, -. doi: 10.22124/jmm.2026.32920.2996
HARVARD
Sheikhi, S., Esmaeili, H. (2026). 'A class of inversion-free iterative methods to find polar decomposition', Journal of Mathematical Modeling, (), pp. -. doi: 10.22124/jmm.2026.32920.2996
CHICAGO
S. Sheikhi and H. Esmaeili, "A class of inversion-free iterative methods to find polar decomposition," Journal of Mathematical Modeling, (2026): -, doi: 10.22124/jmm.2026.32920.2996
VANCOUVER
Sheikhi, S., Esmaeili, H. A class of inversion-free iterative methods to find polar decomposition. Journal of Mathematical Modeling, 2026; (): -. doi: 10.22124/jmm.2026.32920.2996
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