Continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems

[1]  Roy Mathias,et al.  A Chain Rule for Matrix Functions and Applications , 1996, SIAM J. Matrix Anal. Appl..

[2]  Thomas Kailath,et al.  Linear Systems , 1980 .

[3]  Israel Gohberg,et al.  On the local theory of regular analytic matrix functions , 1993 .

[4]  V. Mehrmann,et al.  Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods , 2004 .

[5]  Lloyd N. Trefethen,et al.  Reviving the Method of Particular Solutions , 2005, SIAM Rev..

[6]  Jon Wilkening,et al.  An algorithm for computing Jordan chains and inverting analytic matrix functions , 2007 .

[7]  Christian Hafner,et al.  Band structure computations of metallic photonic crystals with the multiple multipole method , 2002 .

[8]  G. Sleijpen,et al.  An SVD-approach to Jacobi-Davidson solution of nonlinear Helmholtz eigenvalue problems , 2008 .

[9]  Jianhong Wu Theory and Applications of Partial Functional Differential Equations , 1996 .

[10]  W. Beyn An integral method for solving nonlinear eigenvalue problems , 2012 .

[11]  W. Beyn,et al.  Continuation of Low-Dimensional Invariant Subspaces in Dynamical Systems of Large Dimension , 2001 .

[12]  P. Deuflhard Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms , 2011 .

[13]  Leiba Rodman,et al.  Analytic matrix functions with prescribed local data , 1981 .

[14]  Willy Govaerts,et al.  Numerical methods for bifurcations of dynamical equilibria , 1987 .

[15]  Nicholas J. Higham,et al.  Functions of matrices - theory and computation , 2008 .

[16]  Wim Michiels Stability and stabilization of time-delay systems , 2002 .

[17]  E. Allgower,et al.  Numerical Continuation Methods , 1990 .

[18]  Tomaž Košir,et al.  Kronecker Bases for Linear Matrix Equations, With Application to Two-Parameter Eigenvalue Problems , 1996 .

[19]  Luca Dieci,et al.  Continuation of invariant subspaces , 2001, Numer. Linear Algebra Appl..

[20]  Olaf Steinbach,et al.  A boundary element method for the Dirichlet eigenvalue problem of the Laplace operator , 2009, Numerische Mathematik.

[21]  Daniel Kressner,et al.  A block Newton method for nonlinear eigenvalue problems , 2009, Numerische Mathematik.

[22]  H. Keller,et al.  Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem , 1997, SIAM J. Matrix Anal. Appl..

[23]  James Demmel,et al.  Continuation of Invariant Subspaces in Large Bifurcation Problems , 2008, SIAM J. Sci. Comput..

[24]  N. Kamiya,et al.  Generalized eigenvalue formulation of the helmholtz equation by the trefftz method , 1994 .