Previously known as Vishnu Shastri, Madhava Tirtha was the third 'acharya' to reside on the Pitha after the disappearance of Shripad Madhwacharya. It is suggested that a possible time for his birth could be 1136 Sakabja Era (corresponding to 1251 AD.) according to the Bombay Gazzette (A.C. Bhaktivedanta Swami Prabhupada. Shri Chaitanya Charitamrta. Madhya-lila 9:245. purport.)
The senior most direct disciples of Shri Ananda Tirtha (Madhwa) were Shri Padmanbha Tirtha, Shri Narahari Tirtha, Shri Madhava Tirtha and Shri Akshobhya Tirtha. In the same order they were the pontiffs of what latter became known as the Shri Uttaradi Mutt with an ending year of 1324 AD, 1332 AD, 1350 AD and 1365 AD, respectively. Some suggest that Shri Akshobhya Tirtha obtained his sannyasa ashrama from Shri Madhava Tirtha, however from my understanding Akshobhya Tirtha was a sannyasi when Madhwa installed him with the others at Kanva tirtha to be the heads of the various Mutts
As mentioned by Shri Banejee Govindacharyaji, Shri Madhava Tirtha also established the Majjige Halli Mutt near Mulubagal (Karnataka) and deputed Shri Madhurai Tirtha (one of his desciples) to look after the mutt. The Majjige Halli Mutt worships the Veera Rama Idol personally worshipped by Shri Madhava Tirtha. He also started Kanva Mutt.
He also gave 'ashrama' to Shri Akshobhya Tirtha and installed him as the Pith Adipatya or pontiff of Shri Uttaradi Mutt to worship the idols/Deities which were personally worshipped by Shrimad Acharya (Madhwa) himeself.
Once a marvellous incident happened when Shri Madhava Tirtha was engaged in the worship of Digvijaya Rama that Narahari brought back for Madhwa. All of a sudden he moved from his place and made prostration to some great personality visible to himself and invisible to others and sat with folded hands. The whole pooja was over and Shri Madhava Tirtha most reverently took the sacred tirtha (holy water) from one who was invisible. The whole incident was clarified afterwards by Shri Madhava Tirtha himself to satisfy the curiosity of the devout spectators. He said – "The Deity of Vamsha Rama which I have now acquired with Providential grace has been endowed with special sacredness of Shrimad Acharya (Madhwa) who came in person to worship the Deity. He worshipped in his usual grand way, took tirtha (charan-amrita) himself and blessed me with tirtha afterwards". The whole gathering was astounded at the great event. A similar incident was also reported to have been experienced by Shri Akshobya Tirtha when he was worshiiping Shri Prasanna Vittala in Pandarapur..
Shripad Madhava Tirtha was quite often confused with, or known as 'the Madhwacharya' or Madhwa, due to the similarity in name.
The story refered to in this connection of how the other Madhava Tirtha founded the city of Vijayanagar after the discovery of a huge amount of hidden treasure is as follows. Before this, however, Madhava Tirtha lived an austere life as an ascetic in the mountains of Karnataka, who once found himself being frequented by a shepherd of the name Bukka. This poor shepherd had heard that Madhava Tirtha, the great 'sannyasi', was there absorbed in thoughts of Lord Narayana, and so he decided to daily bring him some simple foodstuffs. Madhava Tirtha blessed him saying, "One day you shall be the King of all Industan." By this blessing, immediately all the local shepherds made him their head, and he became known as the King of that local country which governed five groups of communities – Chanara, Taligas, Canguivaro, Negapatao and Badagas. In this kingdom he became known as Boca Rao and reigned for thirty seven years by the blessings of the great Madhava Tirtha. Bukka conquered many kingdoms from the time he came to rule in 1343 A.D.
All that we could find is that Shripad Madhava Tirtha was in office at the Vedanta Pitha from 1333 A.D., until 1350 A.D., when he passed away. Some say that he made a commentary on the Parasara Smrti called Parasara Madhwa-vijaya, and some other books have also been accredited to him (Rg, Yajus and Saama Veda commentaries), most people consider this very complimentary, but possibly unfounded. As little is known of him, there is much confusion maybe mis-identifying him with others.
It is said that his bodily remains were entombed at Hampi, but have since been moved to Manur on the Bhima River of Bijapur District. Very recently, a mritika brindavana of Shri Madhava Tirtha was installed in Mulubagal. He founded a mutt of his own near there under the name of Majjigenahalli Matha just near by Mulbagal and deputed Shri Madhurai Tirtha (one of his desciples) to look after it. The Majjige Halli Mutt worships the Deity of Veera Rama personally worshipped by Shri Madhava Tirtha. He is also reputed by some to have started Kanva Mutt..
The Mahalaya Amavasya (which usually falls in the month of Ashwin) is this great saint's aradhana (disappearance anirversary).
Source : http://www.hknet.org.nz/gp-Madhava%20Tirtha.htm