The Ekoddishta Shraddha of those who have faced unnatural deaths like accidents and suicide must be performed on the 14th tithi of Pitr paksha.
As per the Brahmanda Purana Upodghāta-pāda, Chapter 17:
Śrāddha should be performed on the fourteenth day to those persons in the house who happened to die while young or who had been struck down dead by means of weapons.
As per Chapter 222 of the Nagarakhanda of the Skanda Purāṇa:
येषां च शस्त्रमृत्युः स्यादपमृत्युरथापि वा - O king, Śrāddha should be performed on the Caturdaśī (fourteenth) tithi in the case of those who meet with their death in the following manner: unnatural death, killed by weapons, supernatural calamities, being poisoned...
The reason too has been explained in the same chapter. Brahmaji gave an asura a boon that all the Shraddha offering on chaturdashi tithi shall go to Bhuta, preta, etc. Since after ‘unnatural deaths’, the person generally becomes a Preta, chaturdashi tithi is advised for them after the Sapindikarana rites have been done. (verses 10-24)
Now, the term ‘unnatural death’, which is basically accidents and suicide, is explained in the Garuda Purana, Pretakanda, Chapter 40:
[Garuda Says] भगवन्ब्राह्मणाः केचिदपमृत्युवशं गता:। - Oh Bhagavan, those Brahmins who have gone owing to unnatural death, in what way to they go, to which place and what is their Gati?
[Bhagavan lists cases of unnatural death शृणु तार्क्ष्य परं गोप्यं जाते दुर्मरणे सति] - That Brahmana who dies due to crossing a ditch, river or drain, getting bitten by a snake, by pressing of the throat, drowning in water, with the trunk of an elephant, drinking poison, getting burnt, attack by a bull, Cholera, committing suicide, hanging or drowning, etc. attains Naraka.
As regards the view that Shraaddha should not be performed for those of unnatural death, the Nirnaya Sindhu, Pariccheda 2, Ashivanamasa, Page 237, gives a clarification:
Despite the fact that Chhagaleya says not to do Shraaddha for: Those killed due to weapons, Brahmins, horned and tusked animals, snake venom and those leaving their body themselves; these people who have died owing to such negligence are eligible for Shraaddha and the same must be done. Further the statement that only tarpana and not pinda Dana is not to be performed for such people is a Gauna Paksha (baseless argument).
Thus it is necessary to perform Ekoddishta Shraddha for those who died unnaturally (not untimely, but unnaturally)
It doesn’t vary with married or unmarried. But age can have an effect only on the initial rituals. For example in the case of children (irrespective of natural or unnatural) instead of cremation, burial is advised. In all books, the above tithi is only for unnatural deaths (old or young), not untimely natural deaths, despite the above Brahmanda Purāṇa quote.
Note: As RickRoss says, the rites must not be performed for such people. As per the Shraaddhakalpalata, they should be silently cremated. After performing the necessary prayashchitt, a Narayana Bali should be done. Other rituals like Shraaddha can be performed only if the Narayana Bali has been done at the specified time (within a year) after unnatural death. Because it is only after Narayana Bali that other rites like Sapindikarana, acquire eligibility. The Shraaddhakalpalata Page 104 says that Ekoddishta is to be performed after Sapindikarana (which can be performed only after Narayana Bali). Therefore in case not done, it is first advisable the get the Narayana Bali and other rituals done.