The Gauss pseudospectral method (GPM), one of many topics named after Carl Friedrich Gauss, is a direct transcription method for discretizing a continuous optimal control problem into a nonlinear program (NLP).
[9] More recent work in chemical and aerospace engineering have used collocation at the Legendre–Gauss–Radau (LGR) points.
[17] The CPM uses Chebyshev polynomials to approximate the state and control, and performs orthogonal collocation at the Chebyshev–Gauss–Lobatto (CGL) points.
[18] The LPM uses Lagrange polynomials for the approximations, and Legendre–Gauss–Lobatto (LGL) points for the orthogonal collocation.
[19] Recent work shows several variants of the standard LPM, The Jacobi pseudospectral method[20] is a more general pseudospectral approach that uses Jacobi polynomials to find the collocation points, of which Legendre polynomials are a subset.