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Modified Matrix Factorizations for Solving Systems of Nonlinear Equations
Author(s) -
Hoy A.,
Schwetlick H.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860660702
Subject(s) - cholesky decomposition , convergence (economics) , factorization , mathematics , nonlinear system , matrix (chemical analysis) , incomplete cholesky factorization , computer science , mathematical optimization , process (computing) , order (exchange) , algorithm , eigenvalues and eigenvectors , physics , materials science , finance , quantum mechanics , economics , composite material , economic growth , operating system
The modified Cholesky factorization due to Gill and Murray as well as an adaptation to the case of nonsymmetric LU‐factorizations described in the literature often generate modified Newton directions which are badly scaled. In order to overcome the deficiencies observed a new technique for modifying LU‐factorizations is proposed which avoids extreme differences in the pivot size and, therefore, leads to more balanced directions. Under appropriate assumptions the global convergence is proved. Some numerical examples demonstrate that the new method is suitable to deal with singular points occurring in the intermediate stages of the iterative process.