# The nonlinear eigenvalue problem: recent developments

Given a matrix-valued function F that depend nonlinearly on a single

parameter z, the basic nonlinear eigenvalue problem consists of finding complex scalars z for which F(z) is singular. Such problems arise in many areas of computational science and engineering, including acoustics, control theory, fluid mechanics and structural engineering.

In this talk we will discuss some interesting mathematical properties of

nonlinear eigenvalue problems and then present recently developed

algorithms for their numerical solution. Emphasis will be given to the linear algebra problems to be solved.

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