Predictors and Correctors

Predictors and Correctors

We use a predictor-corrector scheme to track paths. These are the predictors and correctors currently available.

Predictors

The following predictors are currently implemented.

HomotopyContinuation.Euler — Type.
Euler()

This uses the explicit Euler method for prediction, also known as the tangent predictor.

HomotopyContinuation.Heun — Type.
Heun()

The Heun predictor of order 2.

HomotopyContinuation.Ralston — Type.
Ralston()

The Ralston predictor of order 2.

HomotopyContinuation.RK3 — Type.
RK3()

The classical Runge-Kutta predictor of order 3.

HomotopyContinuation.RK4 — Type.
RK4()

The classical Runge-Kutta predictor of order 4.

HomotopyContinuation.Pade21 — Type.
Pade21()

This uses a Padé-approximation of type (2,1) for prediction.

HomotopyContinuation.NullPredictor — Type.
NullPredictor()

A predictor which does no prediction step, i.e., it just returns the input as its prediction.

Correctors

The following correctors are currently implemented.

HomotopyContinuation.NewtonCorrector — Type.
NewtonCorrector(;simplified_last_step=true)

An ordinary Newton's method. If simplified_last_step is true, then for the last iteration the previously Jacobian will be used. This uses an LU-factorization for square systems and a QR-factorization for overdetermined.