TY - JOUR
T1 - Multiple Nonlinear Eigenvalues of Smooth Rank-deficient Matrices
AU - A. Binder & J. Rebaza
JO - International Journal of Numerical Analysis Modeling Series B
VL - 1
SP - 109
EP - 122
PY - 2010
DA - 2010/01
SN - 1
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/328.html
KW - Smooth factorizations
KW - multiple nonlinear eigenvalues
AB - A smooth block LU factorization, coupled with Newton's method, is used to compute multiple nonlinear eigenvalues of smooth rank-deficient matrix functions A($\lambda$). We provide
conditions for such factorizations to exist and show that the algorithm for the computation of
multiple nonlinear eigenvalues converges quadratically, and is more efficient than one using QR
factorizations. A possible approach for cubic convergence is also discussed. Several numerical
examples are given for general and random nonlinear matrix functions A($\lambda$).