From sociological/archaeological points of view this research paper, Ideological Rigidity and the Limits of Ingenuity, by Gary Bowden, University of New Brunswick-Fredericton, is a good read for those with an interest in what may have happened to the Greenland Vikings during the 500-year history of the two known Norse settlements on the southwestern Greenland coast. Bowden has done a good job consolidating the dogma of the current science regarding the disappearance from history of the 4000-6000 Norse Greenlanders.
Bowden's supposition is that the Norse Greenlanders adhered to the pastoral practices of their kin in the homelands, eventually starving as the weather worsened with the advent of the Mini-Ice Age rather than adopt the survival techniques of the Arctic natives. He identifies these natives as Inuit and according to all accepted research on the subject the Inuit did not begin to arrive in the area from the west until the 12th century, so they were not there in sufficient numbers to influence anyone. The Dorset Culture, or Tornit, peopled the Arctic and Greenland when the Norse first arrived in 986: it is they who would have influenced the Norse if anyone did.
I believe that an assimilation process with North American natives began shortly after the Norse arrival on Greenland simply because the environment dictated adaptation rather than adherence to centuries of pastoral subsistence farming. The Norse Greenlanders did not starve out, they assimilated with the natives of North America.