Ultimate Scholar

Chapter 8 Adaptive Viscous Algorithms for Variational Inequalities in Hilbert Spaces



Lin Yao's office.

"You boy, I won't deduct your usual points for being late today, because you did well in the exam this time."

Lin Yao said to Li Mu who was also in the office.

"Thank you, Professor Lin."

Li Mu smiled and said gratefully.

The library was so far away from the classroom, and he didn't have a small e-Donkey, so he arrived a long time late. Who would have thought that Professor Lin inside was praising him?

Then the next two classes passed, and the multivariate calculus class ended.

Then Li Mu was called here by Professor Lin.

Of course, it must be related to this exam.

"Actually, I'm quite curious. Why did you suddenly pass the exam so well this time?"

"Uh...Maybe it's because I've become enlightened during this time?"

Li Mu replied.

Having an extra computer in my mind should be regarded as enlightenment, right?

But Lin Yao didn't think Li Mu's answer was perfunctory, and nodded in agreement: "It's possible, after all, there are such precedents. Of course, the most important thing is your own talent. You have to discover your own talent and make good use of it. It, that's the best."

Lin Yao is not stingy with his recognition of talent. After all, mathematics is like this. The more talented a person is, the easier it is to make achievements, and the more he can bring impetus to the development of mathematics.

"So if you have any problems in the future, you can also come to me. I can provide you with guidance. If it doesn't work, I can also help you find other teachers. Your primary goal is to give full play to your own potential .”

"Thank you professor!"

Hearing Lin Yao's words, Li Mu was slightly moved. Just one test result can make him pay so much attention, which is enough to show that Lin Yao attaches great importance to cultivating students.

Thinking of this, Li Mu hesitated for a moment, remembering the new mission.

Then, he asked, "Professor Lin, I actually have a question that I would like to ask you."

"Oh? Just ask." Lin Yao said with a smile.

As long as there are questions, he was afraid that Li Mu would not ask.

"I want to write a thesis, which topic do you think is better?"

Hearing Li Mu's question, Lin Yao was stunned for a moment, and then laughed.

"Very good, very good."

When I was a freshman, I wanted to write a thesis.

Of course, he didn't think that Li Mu was so ambitious, and he even thought that writing a thesis since freshman year was something worth promoting.

And such a student is also a good student that their teacher likes!

Regarding Li Mu's question, Lin Yao didn't have any secrets, and directly listed a lot of topics.

Although Lin Yao is a professor in the School of Mathematics, he also studies physics, so the topics listed are all related to physics and meet Li Mu's needs.

At the same time, Lin Yao spent nearly an hour giving him guidance, including the analysis of these selected topics, as well as recommended books, recommended reviews, papers and so on.

Under Lin Yao's explanation, Li Mu quickly understood what he needed to do to write a thesis from scratch.

You need to look at the overview, so as to understand the research progress of the selected topic, and also look at the papers on the direction of the selected topic, so as to gather the strengths of a hundred schools of thought, and then form the words of one family.

For Li Mu, who has never written a formal paper, this knowledge is something that needs to be listened to carefully.

After all, these are the experiences of a professor of mathematics at Shanghai Jiaotong University.

Until the end, Li Mu kept all the essentials in his mind, and said gratefully, "Thank you, Professor."

"You're welcome, I'm a teacher and you are a student, so I should teach you as well."

Lin Yao smiled and waved his hands, and said: "Next, you can go back and find your own topic, and then start writing by hand. If you have any questions, you can ask me, and you can also ask on Weixin."

"Good professor."

Li Mu nodded, then took out his mobile phone and added Lin Yao's prestige, then stopped bothering and left.

Next, he will start working hard for his first thesis.

...

Still a library.

Li Mu turned on the GTX960 configuration of his laptop that he asked his family to buy for more than 3,000 yuan before going to college.

This year is 2019, and the 20 series graphics cards have been on the market for half a year, and the 960 has become a treasure of ancient times.

But for him, playing LOL can still pass, let alone writing a paper or something.

The only difference from the fruit computers in front of the other students in the library is that this notebook of his is quite large...

Of course, this does not affect the truth from which it is born.

Create a new folder and name it Papers.

Then create a new word document and enter the document interface.

After thinking for a moment in his heart, he recalled the topics that Lin Yao pointed out to him just now, and finally, he entered the topics he had determined.

Adaptive Viscous Algorithm for Variational Inequality Problems in Hilbert Spaces

【Abstract: A new adaptive hypersubgradient is proposed to solve the pseudo-monotonic variational inequality problem in Hilbert space. Applying the new step size criterion, a strong convergence theorem is obtained without knowing the Lipschitz constant. Some numerical examples illustrate the effectiveness of the proposed algorithm. 】

The abstract and topic selection are based on Professor Lin Yao's recommendation and explanation, and then he decides according to his own ideas.

A topic between mathematics and physics, or rather, it belongs to the content of [Methods of Mathematical Physics].

And the difficulty of this topic...

Li Mu didn't know, but anyway, Lin Yao's evaluation of the original topic was that it was the most difficult of all the topics, and now that he changed it a little, he didn't know how difficult it was.

Probably, it is a little bit more difficult than the original choice?

As for the difficulty of topic selection, it mainly lies in the Hilbert space.

Hilbert space, one of the core concepts of functional analysis, is also mainly used in formulaic mathematics and quantum mechanics.

However, during those seventy-two hours, Li Mu had already read all the books on the knowledge points he needed, such as functional analysis and quantum mechanics.

Although there is no guarantee that the knowledge he has now is enough, what needs to be known is that beside him is a library with a collection of more than three million books!

If he really encountered a problem, he could also gain enough knowledge from the books, not to mention, Professor Lin Yao had recommended a few related books to him just now.

So he didn't worry at all whether the topic selection was too difficult.

Just like that, just do it, and then, he immediately got ready.

First of all, he went to borrow books. According to the book list recommended by Professor Lin Yao, he found books that he might be able to use in this paper, and two of them were English textbooks.

Although the English textbook is a bit of a headache, for him who now has a brain computer, there is no problem in learning the language. With this kind of English textbook, he can learn English while learning the knowledge described in it.

In addition, there are relevant literature.

In this way, if you don’t understand, you can check the books and literature, and if you understand, start writing.

As time passed, he gradually had a clear understanding of the framework of the whole paper from the knowledge he had learned, and began to elaborate on the first two parts.

As for the outline or something, it doesn't exist, because he has all these things in his mind.

Time gradually came to the night.

It's the familiar closing time again.

At least he is very familiar with Li Mu.

After all, he basically ends around this time every night.

Of course, he paid attention to the time a few days ago, but he never forgot, but today, perhaps he suddenly became obsessed with this kind of high-end problem for him, so that he put all his thoughts into it. Among them, the time was not noticed at all.

Just like that, only the sound of his typing was left in the library, until about five minutes later, a girl came over.

Yun Rongshang, librarian.

And it was she who reminded Li Mu to close the library last week night.

This area is the last area she is in charge of, and she can leave after simply tidying up.

It's just that after arriving here, she couldn't help admiring someone who was still studying seriously.

Those who can learn this level are worthy of admiration.

But when she saw Li Mu's face, she was taken aback.

Isn't this the boy from the physics department last week?

In fact, she would come to the library three days a week to take charge, and during these two weeks, she could see Li Mu leaving the library when the library was closed.

"Can people really learn like this?"

There are big doubts in my little heart.

What a fierce man...

But it looks like this person is writing a thesis now?

She stepped forward curiously, took a look, and immediately chose to give up. She is just a finance student and can't see such things.

Then I looked at the various books on the desk next to me. What about functional analysis, Hilbert spaces, variational inequalities... There are even English textbooks? !

It's all stuff that sounds awesome.

What kind of boss is this!

She was stunned.

New books please collect and recommend! !


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