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Sparse quasi‐Newton LDU updates
Author(s) -
Tewarson R. P.,
Zhang Yin
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620240605
Subject(s) - jacobian matrix and determinant , newton's method , algebraic number , algebraic equation , mathematics , computer science , type (biology) , algebra over a field , algorithm , mathematical analysis , pure mathematics , nonlinear system , ecology , physics , quantum mechanics , biology
Numerical solution of a given non‐linear algebraic system of equations by a quasi‐Newton type method requires updating the approximation to the Jacobian at each step. Two methods for large sparse systems are described. The approximation for the Jacobian is factored into an LDU form at the first step, then all the subsequent updates are made to L , D and U . Computational evidence is given exhibiting the relative efficiency of these methods over those currently available in the published literature.