Calculation Of Maximum Eigenvalue Of Nonnegative Matrix And Nonnegative Tensor

Nonnegative matrices are an important matrix class,and the estimation and calculation of their lagest eigenvalues(spectral radius)are the classical content of nonnegative matrices theory research.Meanwhile,as an important extension of nonnegative matrices,their eigenvalues are also widely used in science and engineering,which are a research topic that attracts much attention at present.This essay studies the calculation of the lagest eigenvalues and corresponding eigenvectors of nonnegative matrices and nonnegative tensors,and the main contents are as follows:Firstly,by applying Perron-Frobenius theorem of spectral radius of nonnegative matrices and diagonal similarity transformation of matrices,a more general iterative algorithm of diagonal similarity between the lagest eigenvalues and corresponding eigenvectors of nonnegative matrices are constructed by analysis and theoretical proof.Based on iterative matrix,this algorithm constructs a positive diagonal similarity transformation with variable parameters,which has great flexibility and universality and is suitable for all irreducible nonnegative matrices.Numerical examples further illustrate the feasibility of the algorithm and the influence of parameters on convergence speed.Secondly,by using C-W function,C-W algorithm is constructed to calculate the maximum eigenvalues of irreducible nonnegative matrices,which has a good convergence efficiency.Thirdly,as an application of the lagest eigenvalues algorithm for nonnegative matrices,the iterative discriminant method of M-matrix(generalized strictly diagonally dominant matrix)is given.Fourthly,for the calculation of the lagest eigenvalues and the corresponding eigenvectors of nonnegative tensors,similar to the diagonal similarity transformation of nonnegative matrices,the calculation method of the essentially positive tensors are given.