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Implement boundary oracle for integral collocation method #121
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@vissarion I'd like to know the status of this issue, has it been solved yet? and if not, if I can help. |
Hi @JRS296 thanks for your interest I do not know if this issue is the right to get started. |
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The Integral Collocation method of this paper is implemented in volesti under
include/ode_solvers/integral_collocation.hpp
.The current state of the solver does not include a boundary oracle (and thus it does not currently support truncation).
The goal of this feature request is to implement a boundary oracle for the method.
More specifically the boundary oracle method has to solve the intersection of the trajectory
(computed via Lagrange interpolation at the Chebyshev nodes) which is defined by its
Chebyshev transform (via using the Chebyshev transform class provided in boost) with
the boundary of the H-polytope.
To solve it effectively, I propose converting the Chebyshev transform to a complex polynomial
of twice the degree such that the real part of its roots represent solutions of the equation.
So, all in all, we need to
a[k] x^k -> a[k] / (k + 1) x^{k + 1}
)The text was updated successfully, but these errors were encountered: