<p>In the newest version of this <a href="https://arxiv.org/abs/1612.04208" rel="nofollow noreferrer">paper</a> by Yijie Han, the author claims that matrix multiplication can be solved by an <span class="math-container">$\tilde{O}(n^2)$</span> algorithm. It should be a big result, but it is still in arxiv and no one else ever cited it. I've tried to read it and the basic idea is an <span class="math-container">$O(\log^c{n})$</span> computation for inner product where <span class="math-container">$c$</span> is an constant, which results in an <span class="math-container">$O(n^2\log^c{n})$</span> algorithm for matrix multiplication.</p>
<p>The details in this paper are too complicated to be fully understand, have anyone checked the correctness of this paper or read this paper?</p>

CC BY-SA 4.0
2021-04-22T09:55:17.540Z
Probably people gave up. Notice that this paper 16 different versions and there was an error in each of the versions. Plus the paper seems to be poorly written, there are no lemmas inside etc.
Bartosz Bednarczyk
CC BY-SA 4.0
2021-04-22T10:53:00.277Z
On page 20 of the current version, the author writes: *"Also I have a vague feeling that the matrix multiplication algorithm presented in this paper may have implications to the NP-complete problems."*
Gamow
CC BY-SA 4.0
2021-04-22T10:59:15.687Z
Abstract states inner product in O(1) which means he is ignoring sizes of words.
Turbo
CC BY-SA 4.0
2021-04-22T11:10:29.880Z
@1.. what do you mean by that? Could you please be more specific?
Mengfan Ma
CC BY-SA 4.0
2021-04-28T11:58:55.113Z
[Current](https://www.smbc-comics.com/comic/mathematicians) [state of the art](https://arxiv.org/abs/2010.05846).
J.G.
CC BY-SA 4.0
2021-04-28T12:18:43.183Z
@J.G. I knew the laser method but the Han's paper uses a totally different technology, which I have seen nowhere.
Mengfan Ma
<cc.complexity-theory><matrix-product>
An $O(n^2\log^c{n})$ algorithm for matrix multiplication in this paper?
Mengfan Ma
# An $O(n^2\log^c{n})$ algorithm for matrix multiplication in this paper?

(Asked by: username_0 on 2021-04-22)

In the newest version of this [paper](https://arxiv.org/abs/1612.04208) by Yijie Han, the author claims that matrix multiplication can be solved by an $\tilde{O}(n^2)$ algorithm. It should be a big result, but it is still in arxiv and no one else ever cited it. I've tried to read it and the basic idea is an $O(\log^c{n})$ computation for inner product where $c$ is an constant, which results in an $O(n^2\log^c{n})$ algorithm for matrix multiplication.

The details in this paper are too complicated to be fully understand, have anyone checked the correctness of this paper or read this paper?

**Tags:** cc.complexity-theory, matrix-product
> **Comments:**
> **username_1**: Probably people gave up. Notice that this paper 16 different versions and there was an error in each of the versions. Plus the paper seems to be poorly written, there are no lemmas inside etc.  
> **username_2**: On page 20 of the current version, the author writes: *"Also I have a vague feeling that the matrix multiplication algorithm presented in this paper may have implications to the NP-complete problems."*  
> **username_3**: Abstract states inner product in O(1) which means he is ignoring sizes of words.  
> **username_0**: @1.. what do you mean by that? Could you please be more specific?  
> **username_4**: [Current](https://www.smbc-comics.com/comic/mathematicians) [state of the art](https://arxiv.org/abs/2010.05846).  
> **username_0**: @J.G. I knew the laser method but the Han's paper uses a totally different technology, which I have seen nowhere.  

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## 0 answers

