Volume 1, Issue 1
Multiple Nonlinear Eigenvalues of Smooth Rank-deficient Matrices

Int. J. Numer. Anal. Mod. B, 1 (2010), pp. 109-122

Published online: 2010-01

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• Abstract

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($\lambda$).

• Keywords

Smooth factorizations multiple nonlinear eigenvalues

65F99 35P30

@Article{IJNAMB-1-109, author = {A. Binder and J. Rebaza}, title = {Multiple Nonlinear Eigenvalues of Smooth Rank-deficient Matrices}, journal = {International Journal of Numerical Analysis Modeling Series B}, year = {2010}, volume = {1}, number = {1}, pages = {109--122}, abstract = {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($\lambda$).}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnamb/328.html} }
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($\lambda$).