Email discussion Minutes
August September 2015
Phase flow methods
Every numerical method on a grid of initial points can be collected under the name of “phase flow methods”.
The initial scaling and squaring of Hingram or Molen van Loan is performed on matrices. For Diff, it arises the necessity of considering several starting points.
For Diff Candes exploited the one parameter subgroup properties
Main result: exploiting the one parameter subgroup property for the scaling and squaring approaches. Hingram or Molen van Loan approaches were about matrices and not about SVF.
The main contribution with respect to Vicent Arsigny’s paper is the analysis of the approximation error coming from this scheme + some variants of the approach.
— Bibliography
Steinberg, S. (1984). Lie series and nonlinear ordinary differential equations. Journal of Mathematical Analysis and Applications, 101(1), 39–63. doi:10.1016/0022-247X(84)90057-X
Ying, L., & Candès, E. J. (2006). The phase flow method. Journal of Computational Physics, 220(1), 184–215. doi:10.1016/j.jcp.2006.05.008