SAN FRANCISCO — Apple has fired the manager responsible for its troubled mapping software, seeking to win back the trust of users disappointed after the program debuted in September, according to people familiar with the move.

Richard Williamson, who oversaw the mapping team, was fired by senior vice president Eddy Cue, said the sources, who asked not to be named because the information wasn’t yet public. Cue, who took over last month as part of a management shakeup, is now seeking advice from outside mapping-technology experts and prodding digital maps provider TomTom to fix landmark and navigation data it shares with Apple.