  One of the most challenging computational problems in the Run 3 of the Large
Hadron Collider (LHC) and more so in the High-Luminosity LHC (HL-LHC) is
expected to be finding and fitting charged-particle tracks during event
reconstruction. The methods used so far at the LHC and in particular at the CMS
experiment are based on the Kalman filter technique. Such methods have shown to
be robust and to provide good physics performance, both in the trigger and
offline. In order to improve computational performance, we explored
Kalman-filter-based methods for track finding and fitting, adapted for
many-core SIMD architectures. This adapted Kalman-filter-based software, called
"mkFit", was shown to provide a significant speedup compared to the traditional
algorithm, thanks to its parallelized and vectorized implementation. The mkFit
software was recently integrated into the offline CMS software framework, in
view of its exploitation during the Run 3 of the LHC. At the start of the LHC
Run 3, mkFit will be used for track finding in a subset of the CMS offline
track reconstruction iterations, allowing for significant improvements over the
existing framework in terms of computational performance, while retaining
comparable physics performance. The performance of the CMS track reconstruction
using mkFit at the start of the LHC Run 3 is presented, together with prospects
of further improvement in the upcoming years of data taking.
