Nonlinear Hilbert adjoints: properties and applications to Hankel singular value analysis
Nonlinear Analysis: Theory, Methods & Applications - 1st Level Done by Prameela
From Linear to Nonlinear Large Scale Systems
SIAM Journal on Matrix Analysis and Applications
Mathematics and Computers in Simulation
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Let $A(\lambda )$ be a holomorphic matrix-valued function defined on a domain $\Omega \subset {\Bbb C}.$ The nonlinear eigenproblem of finding generalized eigenpairs $\lambda ,\ v$ such that $A(\lambda )v=0$ is considered. The method which is exposed for solving this problem is based on the derivatives of the function $x(\lambda )=A(\lambda )^{-1}b$, where $b$ is a given vector. Theoretical convergence results are established, and an algorithm is proposed for computing a few eigenvalues close to a given complex number together with some corresponding eigenvectors.