Debate over Initial Settlement of Iceland

Who were the first European settlers to come to Iceland? Were they truly Ingólfur Arnarson his wife Hallgerdur Fródadóttir, as told in Íslendingabók (Book of Icelanders)?

Icelanders have long believed that this pair settled near Rekyavik in 874 and founded what eventually became that city. But both a conflicting legend and new archaeological evidence suggest the possibilility that Irish monks may have been there first. "...Archeologist Bjarni F. Einarsson, who last year studied a settlement building near the church at Kirkjuvogur in Hafnir on the Reykjanes peninsula ... says the building was probably not a farm. It could not have been built later than 880 A.D.