In this paper,a method with parameter is proposed for finding the spectral radius of weakly irreducible nonnegative tensors.What is more,we prove this method has an explicit linear convergence rate for indirectly posi...In this paper,a method with parameter is proposed for finding the spectral radius of weakly irreducible nonnegative tensors.What is more,we prove this method has an explicit linear convergence rate for indirectly positive tensors.Interestingly,the algorithm is exactly the NQZ method(proposed by Ng,Qi and Zhou in Finding the largest eigenvalue of a non-negative tensor SIAM J Matrix Anal Appl 31:1090–1099,2009)by taking a specific parameter.Furthermore,we give a modified NQZ method,which has an explicit linear convergence rate for nonnegative tensors and has an error bound for nonnegative tensors with a positive Perron vector.Besides,we promote an inexact power-type algorithm.Finally,some numerical results are reported.展开更多
基金the Ph.D.Candidate Research Innovation Fund of Nankai University.Qing-Zhi Yang’s work was supported by the National Natural Science Foundation of China(No.11271206)Doctoral Fund of Chinese Ministry of Education(No.20120031110024).
文摘In this paper,a method with parameter is proposed for finding the spectral radius of weakly irreducible nonnegative tensors.What is more,we prove this method has an explicit linear convergence rate for indirectly positive tensors.Interestingly,the algorithm is exactly the NQZ method(proposed by Ng,Qi and Zhou in Finding the largest eigenvalue of a non-negative tensor SIAM J Matrix Anal Appl 31:1090–1099,2009)by taking a specific parameter.Furthermore,we give a modified NQZ method,which has an explicit linear convergence rate for nonnegative tensors and has an error bound for nonnegative tensors with a positive Perron vector.Besides,we promote an inexact power-type algorithm.Finally,some numerical results are reported.
