Jacobian Computation-free Newton ’ s Method for Systems of Nonlinear Equations

@inproceedings{WAZIRI2010JacobianCN,
  title={Jacobian Computation-free Newton ’ s Method for Systems of Nonlinear Equations},
  author={WAZIRI and Leong and Hassan and MONSI},
  year={2010}
}
  • WAZIRI, Leong, +1 author MONSI
  • Published 2010
We propose a modification to Newton’s method for solving nonlinear equations, namely a Jacobian Computation-free Newton’s Method . Unlike the classical Newton’s method, the proposed modification neither requires to compute and store the Jacobian matrix, nor to solve a system of linear equations in each iteration. This is made possible by approximating the Jacobian inverse to a diagonal matrix without computing the Jacobian. The proposed method turns out to be significantly cheaper than Newton’s… CONTINUE READING

References

Publications referenced by this paper.
Showing 1-10 of 10 references

Inexact Newton methods

  • R. S. Dembo, S. C. Eisenstat, T. Steihaug
  • SIAM Journal of Numerical Analysis 19,
  • 1982
Highly Influential
3 Excerpts

Incomplete series expansion for function approximation

  • A. Albert, J. E. Snyman
  • Structural and Multidisciplinary Optimization 34,
  • 2007
1 Excerpt

and Z

  • N. Krejić
  • Lužanin, Newton-like method with modification of…
  • 2002
3 Excerpts

Quasi-Newton’s method with corrections

  • H. Drangoslav, K. Natasa
  • Novi Sad Journal of Mathematics 26,
  • 1996
2 Excerpts

Inexact trust region method for large sparse systems of nonlinear equations

  • L. Lukšan
  • Journal of Optimization Theory and Applications…
  • 1994
3 Excerpts

Numerical Methods for Unconstrained Optimization and Nonlinear Equations

  • J. E. Dennis
  • Prince-Hall, Englewood Cliffs, N J
  • 1983
1 Excerpt

On the convergence of a Quasi-Newton’s method for sparse nonlinear systems

  • L. Binh
  • Mathematics of Computation 32,
  • 1978
1 Excerpt

Similar Papers

Loading similar papers…