Auto-center map with multiple markers in Google Maps API v3

This is what I use to display a map with 3 pins/markers:

<script>
  function initialize() {
    var locations = [
      ['DESCRIPTION', 41.926979, 12.517385, 3],
      ['DESCRIPTION', 41.914873, 12.506486, 2],
      ['DESCRIPTION', 41.918574, 12.507201, 1]
    ];

    var map = new google.maps.Map(document.getElementById('map'), {
      zoom: 15,
      center: new google.maps.LatLng(41.923, 12.513),
      mapTypeId: google.maps.MapTypeId.ROADMAP
    });

    var infowindow = new google.maps.InfoWindow();

    var marker, i;

    for (i = 0; i < locations.length; i++) {
      marker = new google.maps.Marker({
        position: new google.maps.LatLng(locations[i][1], locations[i][2]),
        map: map
      });

      google.maps.event.addListener(marker, 'click', (function(marker, i) {
        return function() {
          infowindow.setContent(locations[i][0]);
          infowindow.open(map, marker);
        }
      })(marker, i));
    }
  }

  function loadScript() {
    var script = document.createElement('script');
    script.type="text/javascript";
    script.src="https://maps.googleapis.com/maps/api/js?v=3.exp&sensor=false&" + 'callback=initialize';
    document.body.appendChild(script);
  }

  window.onload = loadScript;
</script>

<div id="map" style="width: 900px; height: 700px;"></div>

What I’m looking for is a way to avoid having to “manually” find the center of the map with center: new google.maps.LatLng(41.923, 12.513). Is there a way to automatically have the map centered on the three coordinates?