Numerical methods for spectral problems: theory and applications
The numerical methods for nonlinear eigenvalue problems
*Ching-Sung Liu (National University of Kaohsiung, Taiwan)
In this talk, we will introduce nonlinear eigenvalue problems, including tensor eigenvalue problems and nonlinear Schrödinger equations. We will discuss its numerical methods and some numerical results. A great advantage of this method is that it converges quadratically and is positivity preserving in the sense that the vectors approximating the Perron vector (or the ground state vector) are strictly positive in each iteration.