Condition Estimates for Pseudo-Arclength Continuation

@article{Dickson2007ConditionEF,
  title={Condition Estimates for Pseudo-Arclength Continuation},
  author={K. I. Dickson and C. T. Kelley and Ilse C. F. Ipsen and Ioannis G. Kevrekidis},
  journal={SIAM J. Numerical Analysis},
  year={2007},
  volume={45},
  pages={263-276}
}
We bound the condition number of the Jacobian in pseudo-arclength continuation problems, and we quantify the effect of this condition number on the linear system solution in a Newton-GMRES solve. Pseudo-arclength continuation solves parameter dependent nonlinear equations G(u, λ) = 0 by introducing a new parameter s, which approximates arclength, and viewing the vector x = (u, λ) as a function of s. In this way simple fold singularities can be computed directly by solving a larger system F (x… CONTINUE READING

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