According to Gururatnamalika of Sadasiva Brahmendra (verse no.75) and the Sushama commentary on the same by Atmabodha, Vidyaranya, the disciple of Vidyatirtha, Peethadhipathi of the Kanchi Kamakoti Peeta – went to Mysore which was then in a state of confusion, established 8 branch mathas there, Virupaksha and Pushpagiri being two among them.
As regards these two mathas, Kokkandram Venkataratnam Pantulu, an adherent of Sringeri Matha in his Sankara Matha -Tatva- Prakasikartha-Sangraha quotes from the Mathamnaya recited in Pushpagiri Matha according to which Sri Vidyaranya went from Kanchi and installed Chandrasekhara Bharati at Sringeri. He also established a new Matha at Virupaksha where he installed Narasimha Bharati as the Head.
Another version about the origin of this Sankarite institution is as given below:
One of the successors of Narasimha Bharati in the Virupaksha Matha went on tour and on his way he reached Pushpagiri. He found that it was a convenient place for tapas and meditation and accordingly founded a matha there and himself stayed in that (Pushpagiri) Matha and sent one of his disciples to preside over the Virupaksha Matha.
In the Topographical list of inscriptions of the Madras Presidency, many records with names of Narasimha Bharati and Vidyasankara Bharati, the Gurus of Pushpagiri matha, are found. All these Grant’s were made to the Pushpagiri matha, only as an * independent religious institution* .
None of these records mention this matha as a shakha or branch matha of any other Sankarite institution.