# Giampaolo Mele: Krylov methods for nonlinear eigenvalue problems and matrix equations

**Time: **
Thu 2019-11-28 14.15 - 15.00

**Location: **
KTH, F11

**Lecturer: **
Giampaolo Mele, KTH

**Abstract**

Nonlinear eigenvalue problems (NEPs) arise in many fields of science and engineering. In the applications, such problems are often defined by large and sparse matrices. Likewise the linear eigenvalue problem, the eigenvector appears in a linear form, whereas the eigenvalue appears in a nonlinear form. This feature allows the extension of several methods, which are originally derived for the linear eigenvalue problem, to the nonlinear case. Among these methods, Krylov algorithms have been successfully extended in various way. In this talk I will present, and analyze, methods for solving NEPs. In certain applications, solving linear matrix equations is part of the process of solving a NEP. Specialized methods for solving specif matrix equations will be discussed.