There are good reasons to assume that the author was Óláfr Þórðarson (d. 1259), nicknamed hvítaskáld "the White Poet", who was a nephew of Snorri Sturluson.
One of those fragments is also quoted in the Third Grammatical Treatise by Óláfr Þórðarson while an additional fragment is quoted in Laufás-Edda.
Guðjón Þórðarson | Óláfr Þórðarson | ''King Olaf presenting a sword to Sigvatr Þórðarson'', Christian Krohg |