| 摘要 |
Roughly described, a method for numerically solving a system of equations of the form <?in-line-formulae description="In-line Formulae" end="lead"?>0=F(X), <?in-line-formulae description="In-line Formulae" end="tail"?> for a solution vector X which involves choosing a starting value X<SUB>0 </SUB>and iterating <?in-line-formulae description="In-line Formulae" end="lead"?>X<SUB>n+1</SUB>=X<SUB>n</SUB>-[F'(X<SUB>n</SUB>)+sigma<SUB>n</SUB>DiagF'(X<SUB>n</SUB>)]<SUP>-1</SUP>F(X<SUB>n</SUB>). <?in-line-formulae description="In-line Formulae" end="tail"?> In this iteration, at least one sigma<SUB>n </SUB>is a number greater than 0. Preferably, <?in-line-formulae description="In-line Formulae" end="lead"?>sigma<SUB>n</SUB>=min{beta/n, [alphan/(1+nalpha<SUB>n</SUB>)]∥F(X<SUB>n</SUB>)∥}, <?in-line-formulae description="In-line Formulae" end="tail"?> where beta is a constant that remains fixed for all n, and <?in-line-formulae description="In-line Formulae" end="lead"?>alpha<SUB>n</SUB>=∥F(X<SUB>n</SUB>)∥/∥F(X<SUB>n-1</SUB>)∥. <?in-line-formulae description="In-line Formulae" end="tail"?>
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