Purpose – In this study, we present a novel parametric iterative method for computing the polar decomposition and determining the matrix sign function. Design/methodology/approach – This method demonstrates exceptional efficiency, requiring only two matrixby- matrix multiplications and one matrix inversion per iteration. Additionally, we establish that the convergence order of the proposed method is three and four, and confirm that it is asymptotically stable. Findings – In conclusion, we extend the iterative method to solve the Yang-Baxter-like matrix equation. The efficiency indices of the proposed methods are shown to be superior compared to previous approaches. Originality/value – The efficiency and accuracy of our proposed methods are demonstrated through various high-dimensional numerical examples, highlighting their superiority over established methods.
