Chebyshev2.h File Reference

Pseudo-spectral parameterization for Chebyshev polynomials of the second kind. More...

#include <gtsam/base/Manifold.h>
#include <gtsam/base/OptionalJacobian.h>
#include <gtsam/basis/Basis.h>

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Classes
class	gtsam::Chebyshev2

Namespaces
	gtsam
	traits

Detailed Description

Pseudo-spectral parameterization for Chebyshev polynomials of the second kind.

In a pseudo-spectral case, rather than the parameters acting as weights for the bases polynomials (as in Chebyshev2Basis), here the parameters are the values at a specific set of points in the interval, the "Chebyshev points". These values uniquely determine the polynomial that interpolates them at the Chebyshev points.

This is different from Chebyshev.h since it leverage ideas from pseudo-spectral optimization, i.e. we don't decompose into basis functions, rather estimate function values at the Chebyshev points.

Please refer to Agrawal21icra for more details.

Author

Varun Agrawal, Jing Dong, Frank Dellaert

Date

July 4, 2020

Definition in file Chebyshev2.h.