Add Sequential Number to Column

I need to update a non-uniquely indexed column with a sequential number. I think I can do it with the following statement, but I am concerned about performance, since there are about 3 million rows. Is there a faster way to do it than SQL?

update mytable t
set sequence_nbr = ( select count(rowid)

                     from mytable t2
                     where t2.name = t.name
                     and t2.starting_date = t.starting_date
                     and t2.rowid <= t.rowid)
where exists ( select NULL
               from mytable t3
               where t3.name = t.name
               and t3.starting_date = t.starting_date
               and t3.rowid <> t.rowid)