# Main stages in vertex fitting

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The task is, given a set of tracks, to compute the best estimate of the vertex parameters (position, covariance matrix, constrained track parameters and their covariances) as well as indicators of the fit success (total chi^2, number of degrees of freedom, track weights). If so designed, it can decides which track to use and with which weight.

## Steps involved in vertex fitting

Vertex fitting proceeds in several steps, controlled by the VertexFitter. Internally, these steps are implemented in several algorithm classes, which use intermediate reconstructed objects internally. Vertex fitting algorithms are configured with the algorithm which is suited to their needs, so that users should not have to worry about a proper choice. These classes are only used internally by the VertexFitter and are not meant to be used directly. The algorithm classes and internal objects are described further in this section.

1. Linearization point search: if no initial position is provided, search for the linearization point. This is done by a LinearizationPointFinder, whose task is, given a set of tracks, to compute in a very short time a coarse approximation of the vertex position. Several concrete implementations exist, differing mainly by their sensitivity to tracks not belonging to the vertex.

1. Linearization: linearization of the equations which relate the vertex parameters to the track parameters.

1. Track weight: in non-linear algorithms, computation of the track weights.

1. Estimation of the vertex: Track-by-track sequential update of the vertex parameters (VertexUpdator)

1. Vertex smoothing: computation of the track parameters with the vertex constraint and their covariance. This is done by a VertexSmoother. (The class DummyVertexSmoother is provided for the case where this step is not required in a fit. This can be supplied to the VertexFitter, and no smoothing will be done.)

Steps 2-4 are repeated until of the vertex position and covariance matrix converge.

The main components of vertex fitting are:

Internal reconstruction objects: