Positive eigenvector of nonlinear perturbations of nonsymmetric \(M\)-matrix and Newton iterative solution
This paper concerns nonlinear perturbations of nonsymmetric \(M\)-matrices and their Newton iterative solutions, as needed in modeling the Bose-Einstein condensation of matter at near absolute zero temperatures. It is shown that any number greater than the smallest positive eigenvalue of the \(M\)-matrix is an eigenvalue of the nonlinear problem and that the corresponding positive eigenvector is unique and the Newton iteration of the positive eigenvector is convergent. Moreover, such positive eigenvectors form a monotone increasing and continuous function of the corresponding eigenvalues.
scientific article; zbMATH DE number 5289106
scientific article