4 ms·
Many, many, very smart people have worked on exactly this problem and the result is a large, somewhat disjoint, family of techniques for forming/applying approx
by math_and_stuff 10y ago
Many, many, very smart people have worked on exactly this problem and the result is a large, somewhat disjoint, family of techniques for forming/applying approximate inverses in subquadratic time for delicate families of matrices (e.g., discretizations of elliptic partial differential equations).
Keep in mind that many linear systems can be solved in near linear time despite the inverse being dense.
- pmarreck 10y ago> Many, many, very smart people have worked on exactly this problem If I applied this logic to anything genuinely new that was ever discovered, then nothing genuinely new would ever be discovered. I don't know what the fallacy there is, but it must be one. Modern example: Many, many, MANY people worked on globally disparate data synchronization (consensus) problems (Raft, Paxos were some solutions), while ensuring their security, and then Bitcoin came along. Bitcoin hasn't been hacked (although its exchanges have). I'm just saying my gut says there's more to discover there.