Simplicial continuation, or piecewise linear continuation (Allgower and Georg),[1][2] is a one-parameter continuation method which is well suited to small to medium embedding spaces. The algorithm has been generalized to compute higher-dimensional manifolds by (Allgower and Gnutzman)[3] and (Allgower and Schmidt).[4]
The algorithm for drawing contours is a simplicial continuation algorithm, and since it is easy to visualize, it serves as a good introduction to the algorithm.
- ^ Eugene L. Allgower, K. Georg, "Introduction to Numerical Continuation Methods", SIAM Classics in Applied Mathematics 45, 2003.
- ^ E. L. Allgower, K. Georg, "Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations", SIAM Review, Volume 22, 28-85, 1980.
- ^ Eugene L. Allgower, Stefan Gnutzmann, "An Algorithm for Piecewise Linear Approximation of Implicitly Defined Two-Dimensional Surfaces", SIAM Journal on Numerical Analysis, Volume 24, Number 2, 452-469, 1987.
- ^ Eugene L. Allgower, Phillip H. Schmidt, "An Algorithm for Piecewise-Linear Approximation of an Implicitly Defined Manifold", SIAM Journal on Numerical Analysis, Volume 22, Number 2, 322-346, April 1985.