This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors wit...This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.展开更多
In this paper, we present some new perturbation bounds for subunitary polar factors in a special unitarily invariant norm called a Q-norm. Some recent results in the Frobenius norm and the spectral norm are extended t...In this paper, we present some new perturbation bounds for subunitary polar factors in a special unitarily invariant norm called a Q-norm. Some recent results in the Frobenius norm and the spectral norm are extended to the Q-norm on one hand. On the other hand we also present some relative perturbation bounds for subunitary polar factors.展开更多
In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unit...In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.展开更多
基金funded by Iran National Science Foundation(INSF)under project No.4013447.
文摘This study aims to investigate the polar decomposition of tensors with the Einstein product for thefirst time.The polar decomposition of tensors can be computed using the singular value decomposition of the tensors with the Einstein product.In the following,some iterative methods forfinding the polar decomposi-tion of matrices have been developed into iterative methods to compute the polar decomposition of tensors.Then,we propose a novel parametric iterative method tofind the polar decomposition of tensors.Under the obtained conditions,we prove that the proposed parametric method has the order of convergence four.In every iteration of the proposed method,only four Einstein products are required,while other iterative methods need to calculate multiple Einstein products and one tensor inversion in each iteration.Thus,the new method is superior in terms of efficiency index.Finally,the numerical comparisons performed among several well-known methods,show that the proposed method is remarkably efficient and accurate.
基金the Natural Science Foundation of Guangdong Province (31496Natural Science Forndation of University of Teachers of Guangdong Province (0119)Excdllent Talents Foundation of Guangdong Province (Q02084)
文摘In this paper, we present some new perturbation bounds for subunitary polar factors in a special unitarily invariant norm called a Q-norm. Some recent results in the Frobenius norm and the spectral norm are extended to the Q-norm on one hand. On the other hand we also present some relative perturbation bounds for subunitary polar factors.
文摘In this paper,a new matrix decomposition called the weighted polar decomposition is considered.Two uniqueness theorems of weighted polar decomposition are presented,and the best approximation property of weighted unitary polar factor and perturbation bounds for weighted polar decomposition are also studied.
