Directional Newton methods in n variables

Yuri Levin, Adi Ben-Israel

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Directional Newton methods for functions f of n variables are shown to converge, under standard assumptions, to a solution of f(x) = 0. The rate of convergence is quadratic, for near-gradient directions, and directions along components of the gradient of f with maximal modulus. These methods are applied to solving systems of equations without reversion of the Jacobian matrix.

Original languageEnglish (US)
Pages (from-to)251-262
Number of pages12
JournalMathematics of Computation
Issue number237
StatePublished - 2002

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


  • Newton method
  • Single equations
  • Systems of equations


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