Everyone in the audience fell silent and stared at the solution steps given by Xiao Yi on the blackboard.
That's it... is it done?
Is it a little too fast?
Zhang Yitang also looked carefully at the steps he wrote out personally, thinking carefully about the meaning of each step.
However, no matter how he thought about it, there was only one thought in his mind: can the problem of higher-order terms be solved in this way?
How was he thinking before...
Well, he couldn't figure it out before.
In the first row below, Enrique Bombieri, Pierre Deligne and many other big guys are also there.
Looking at the solution given by Xiao Yi, they squinted their eyes. After thinking for a moment, they could only sigh.
"Sure enough, for a problem like this, this guy is still needed." Deligne shook his head and sighed.
Bombieri also nodded. "Who says it's not the case?"
He thought carefully about Xiao Yi's method, and suddenly said, "Do you think that his method, even if it is applied to Fourier expansion itself, seems to be able to solve the problem of error accumulation?"
"Really?" Deligne took another look. After thinking for a moment, his eyes lit up. "Yes, it is indeed true!"
At the same time, other people discovered this, and someone immediately stood up and asked, "Mr. Xiao, if your method can be used to solve the problem on Circle Method Expansion, then can we also use it on Fourier expansion, and can it also be used to solve the problem of error accumulation?"
Regarding this question, Xiao Yi did not have any surprises. He smiled and nodded, "Yes, you discovered it very quickly. The two are closely connected. Of course, some small changes need to be made to it in the process."
"Can you please give us a demonstration?" The questioner said excitedly, "This is very important to me. I feel that it can help me complete my project."
"Of course it's no problem." Xiao Yi smiled and nodded, "Professor Zhang, I still have to trouble you."
Zhang Yitang also came back from his thoughts and said, "No trouble, this also inspired me, tell me."
"Yeah." Xiao Yi then continued.
"First of all, by combining the sieving method with the weighting technology just mentioned, we can get: [g(x)=n=N∑Ndnn(x)+∣n∣>N∑1+∣n∣kcnn(x)]"
"The error control effect is verified by calculating EN′(x). Due to the introduction of w(n), the influence of higher-order terms is significantly weakened, thus ensuring the accuracy of the overall result."
[EN′(x)=|n|>N∑dnn(x)=|n|>N∑1+|n|kcnn(x)]
"..."
Following Xiao Yi's narration, Zhang Yitang also continued to write on the blackboard.
Everyone in the audience started thinking.
Although they may not understand Circle Method Expansion, there are quite a few people who understand Fourier expansion.
As a very classic mathematical method, it can express a periodic function as an infinite series of sine and cosine functions, and has been used to solve various problems.
As for the high-order term problem of Fourier expansion, it mainly involves the impact of high-frequency components in the Fourier series on the accuracy of function reconstruction. People who know it should have heard of Gibbs phenomenon, which is a manifestation of the high-order term problem.
It can be said that people in the mathematical community often have headaches because of this problem when using this method.
Now that this problem seems to have been greatly solved, why don't they listen carefully?
Maybe, just like the questioner, it can help them solve a problem in the subject in the future.
"... In short, that's it. According to the above method, we can weaken the high-frequency terms and stabilize the accumulated error."
"Thus achieving control of the high-order term problem in Fourier expansion."
About ten minutes later, Xiao Yi's story ended.
He smiled and said, "Of course, I think there are still many places that can be explored to further reduce the impact of high-order terms. However, time is limited, so I will stop here for now. I believe you can find them."
"Any other questions?"
He glanced at the mathematicians present.
Time passed quickly, and no one asked any more questions. At the same time, most people were recording what Xiao Yi just said without any distractions.
After a while, Zhang Yitang smiled and said, "It looks like it's gone."
"That's fine." Xiao Yi nodded, and then dozed deeply. "It seems I can go and rest."
"Haha, then you should go to bed early." Zhang Yitang said with a smile, "Oh, by the way, at the end, I would also like to ask you on behalf of the mathematics community, what problems have you been studying recently? Now we are all a little unaccustomed to not seeing your results for so long."
"Uh..." Xiao Yi touched his nose slightly awkwardly and said, "In short, it should be a very important thing, but this thing is more application-oriented."
"You should be able to see him soon."
"Haha, okay, then we are looking forward to it."
Zhang Yitang nodded, then looked at the scholars present and said, "By the way, don't forget to give applause to our Xiao Yi, thanking him for taking the time to answer our questions!"
After saying that, he took the lead in applauding.
The hundreds of mathematicians present also reacted and applauded one after another.
Listening to the applause, Xiao Yi smiled, "Thank you everyone."
As the applause gradually subsided, they finally said goodbye and hung up the phone.
"Hmm... I'm really not used to it."
Xiao Yi turned off the computer and sighed.
If it were live, he would have been able to answer the question on the blackboard with his own hands. Unfortunately, it was a live answer now, so he could only ask Zhang Yitang to write it for him.
Turning around, he saw three people from behind, Ye Cheng, staring at him in shock.
He waved his hand. "Wake up, what are you thinking about?"
The three people finally came to their senses, and Ye Cheng said blankly, "Is this... what it feels like to give a report on stage?"
Song Ziyang also swallowed. "Hundreds of people are looking at me... I feel so stressed."
Luo Qiao: "Brother Xiao, don't you feel nervous being surrounded by so many people?"
"Uh..." Xiao Yi shrugged, spread his hands and said, "There are only a few hundred people, probably less than 400 people, so that's it."
Three people. "..."
Then they all gave Xiao Yi a middle finger.
Pooh!
It was already getting late, so they no longer wasted time and went to rest early. After all, Ye Cheng would have a damn early morning tomorrow.
However, even though Xiao Yi is not in class, they can't say they are envious. After all... Xiao Yi might have gotten up earlier than them.
A night of silence.
The next day, Xiao Yi wrote his Absolute Electronic Computation model 1.0, and then put it on the server and started running it.
Now, all the data of Yishui Bit is placed with Luoming Data Center, which means that his server worth more than 6 million yuan no longer needs to continue to run, and naturally becomes a dedicated server specifically used to run models.
This model is just perfect for feeding him.
And Luo Mingya gave him a lot of experimental data, enough for his model to learn various types of materials.
Probably the only problem is that this model needs to run 24 hours a day for a week.
Of course, it's only a week, not too long.
Let him use the next time to study Goldbach Conjecture.
Recalling the inspirations he had when studying Xiao's expansion and the circle method, he believed that there were many things worth exploring.
In this way, a week passed quietly.
When Xiao Yi came to the Entrepreneurship Center again, he came to room 232 where he was.
"Huh? Why is the server silent?"
Xiao Yi frowned. Logically speaking, the server's fan should be spinning?
"Could it be that there was a power outage last night?"
He immediately hugged his head.
Isn't it?
Although he added a checkpoint saving mechanism, this obviously also wastes a lot of time.
He hurriedly ran over, took a look, and then breathed a long sigh of relief.
"It turned out that the training was completed. It was really scary."
Feeling relaxed, he then opened the trained Absolute Electronic Computation model.
"The next step is to determine whether this model achieves the desired effect... Well, let's give it a try first."
Xiao Yi thought for a while, and then selected two relatively simple materials, silicon and copper.
As a good semiconductor material, silicon has a measured band gap energy of 1.1eV, while copper, as an excellent conductor, has a conductivity of 5.8*10^7S/m.
Now let's use Absolute Electronic Computation to calculate these two materials.
Soon, the results came out.
It is calculated that the band gap energy of silicon is 1.09eV, while the conductivity of copper is 5.78*10^7S/m!
The error rate is less than 1%!
Xiao Yi's eyes suddenly lit up.
This result is really...
Far more than any other computing model!
And the most important thing is that its calculation speed is also very fast, which fully demonstrates that Absolute Electronic Computation not only achieves stable efficiency, but also makes full use of computing resources!