Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지

AN ABS ALGORITHM FOR SOLVING SINGULAR NONLINEAR SYSTEMS WITH RANK DEFECTS

  • Ge, Rendong (Department of Applied Mathematics, Dalian University of Technology) ;
  • Xia, Zun-Quan (Department of Applied Mathematics, Dalian University of Technology)
  • Published : 2003.05.01

⟨ Previous Next ⟩

Abstract

A modified ABS algorithm for solving a class of singular non-linear systems, $F(x) = 0, $F\;\in \;R^n$, constructed by combining the discreted ABS algorithm and a method of Hoy and Schwetlick (1990), is presented. The second differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.

Keywords

References

  1. Numerische Mathematik v.45 A class of direct methods for linear equations J. Abaffy;C.G. Broyden;E. Spedicato
  2. Numerische Mathematik v.51 The local convergence of ABS methods for non-lonear algebraic equations J. Abaffy;A. Galantai;E. Spedicato
  3. ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Equations J. Abaffy;E. Spedicato
  4. OMS v.4 The global convergence of the ABS methods for a class of nonlinear problems A. Galantai
  5. QDMSIA v.40 no.99 Perturbation theory for full rank factorizations A. Galantai
  6. Computing v.40 A relation between Newton and Gauss-Newton steps for Singular nolinear equations A. Hoy
  7. Computing v.41 An efficiently implementableGauss-Newton-like method for solving singular nonlinear equations A. Hoy
  8. Lectures in Applied Mathematics v.26 Some superlinearly convergent methods for solving singular nonlinear equations A. Hoy;H. Schwetlick
  9. J. of Numer. Math. of Chinese Universities v.13 no.1 Modified ABS methods for nonlinear systems without evaluating Jacobian matrices Z. Huang
  10. Optimization Methods and Software v.8 ABS algorithms from Luoyang to Beijing E. Spedicato
  11. To appear Twenty years of ABS algorithms: a bibliography E. Spedicato
  12. Numerical Linear Algebra with Applications v.13 A calss of difference ABS-type algorithms for a nonlinear system of equations E. Spedicato;Z. Chen;N. Deng
  13. QDMSIA v.33 no.96 A new nonlinear ABS-type algorithm and its conver-gence property E. Spedicato;Z. Chen;N. Deng
  14. QDMSIA v.5 Numerial ezperience with Newton-like methods for nonlinear algebraic equations E. Spedicato;Z. Huang
  15. Korean J. Comput. & Appl.Math v.9 no.1 An ABS algorithm for solving sigular nonlinear systems with rank one defect Rendong Ge;Zunquan Xia