Then that would be pitching yeast. Not a starter!
Remember yeast cells bud/multiply depending upon how much food/sugar and oxygen is available to the cell walls (cell walls take in sugar so the more cells per ml of wort = less budding) So.... pitching a vial (if fresh 100 billion cells) of yeast (enough for 19L) to 1 litre of wort is not going to result in much reproduction.
Benefits of using a starter made from something foreign (ie: not the wort you made)?? Meeeeh!!!
Much better to remove two or three litres of your wort post boil, chill to room temp, pitch your yeast and then once the starter is active (about 8 hrs) pitch this "starter wort" to the remainder of the wort in your fermenter.
The method of pitching yeast to 1 litre and letting it ferment out, pouring off the wort and adding the remaining yeast is a good method of conditioning the yeast if it's not really fresh.
Yeast makes beer! So pitch as fresh as you can get and pitch plenty of it!!
Screwy