Chebyshev2.h File Reference

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

Go to the source code of this file.

Classes
class	gtsam::Chebyshev2
	Chebyshev Interpolation on Chebyshev points of the second kind Note that N here, the number of points, is one less than N from 'Approximation Theory and Approximation Practice by L. More...

Namespaces
namespace	gtsam
	Global functions in a separate testing namespace.

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 parameters that enforce function nodes at Chebyshev points.

Please refer to Agrawal21icra for more details.

Author

Varun Agrawal, Jing Dong, Frank Dellaert

Date

July 4, 2020