Krylov methods for the nonlinear eigenvalue problem (Karl Meerbergen - KU Leuven)

02.05.2017 14:15

The nonlinear eigenvalue problem arises from applications in physics and mechanical and civil engineering. In this talk, we discuss how such problems can be solved by using tools for linear eigenvalue problems. The solution takes place in three steps. First, the nonlinear eigenvalue problem is approximated by a matrix polynomial or rational matrix polynomial. Second, this polynomial eigenvalue problem is transformed to a linear problem, called a linearization. In the third step, the linearization is solved by a Krylov method. The size of this linearization is much larger than the size of the matrix from the original nonlinear eigenvalue problem. We discuss how the special structure of the linearization can be used to solve the problem efficiently. We also show relations with other methods for solving nonlinear eigenvalue problems.

Lieu

salle 623, Séminaire d'analyse numérique

entrée libre