The theory of Newton's method

[摘要] We review the most important theoretical results on Newton's method concerning the convergence properties, the error estimates, the numerical stability and the computational complexity of the algorithm. We deal with the convergence for smooth and nonsmooth equations, underdetermined equations, and equations with singular Jacobians. Only those extensions of the Newton method are investigated, where a generalized derivative and or a generalized inverse is used. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-12-01