Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9511520 | Applied Numerical Mathematics | 2005 | 10 Pages |
Abstract
The convergence of Newton's method to a solution xâ of f(x)=0 may be unsatisfactory if the Jacobian matrix fâ²(xâ) is singular. When the rank deficiency is one, and a simple regularity condition is satisfied at xâ, it is possible to define a bordered system for which Newton's method converges quadratically [Griewank, SIAM Rev. 27 (1985) 537]. In this paper we extend this technique to the case of higher rank deficiencies. We show that if a generalized regular singularity condition is satisfied then one singular value decomposition of fâ²(x¯) for some point x¯ near xâ can be used to form a bordered system for which Newton's method converges quadratically. The theory and method are illustrated by several examples.
Keywords
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Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Yun-Qiu Shen, Tjalling J. Ypma,