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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 values at the Chebyshev points.

Please refer to Agrawal21icra for more details.

Author
  Varun Agrawal, Jing Dong, Frank Dellaert

Date
  July 4, 2020