Simplicial or piecewise linear continuation Numerical continuation

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simplicial continuation, or piecewise linear continuation (allgower , georg) based on 3 basic results.


the first is





the second result is:





please see article on piecewise linear continuation details.


with these 2 operations continuation algorithm easy state (although of course efficient implementation requires more sophisticated approach. see [b1]). initial simplex assumed given, reference simplicial decomposition of ir^n. initial simplex must have @ least 1 face contains 0 of unique linear interpolant on face. other faces of simplex tested, , typically there 1 additional face interior zero. initial simplex replaced simplex lies across either face containing zero, , process repeated.





references: allgower , georg [b1] provides crisp, clear description of algotihm.







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