محاسبات عددی علم و هنر محاسبه است. محاسبات عددی (یا آنالیز عددی) به مطالعه ی روش ها و الگوریتم هایی گفته می شود که تقریب های عددی (در مقابل جواب های تحلیلی) را برای مسائل ریاضی بکار می برند. محاسبات عددی با اعمال شیوه های تقریبی محاسباتی به حل مسائلی از ریاضیات پیوسته می پردازد که به روش تحلیلی قابل حل نبوده و یا به سختی قابل حل تحلیلی هستند.
سرفصل هایی که در این آموزش به آن پرداخته شده است:
درس اول: خطاها و اشتباهات
درس دوم: حل دستگاه های معادلات خطی
درس سوم: درون یابی و برازش
درس چهارم: مشتق گیری و انتگرال گیری عددی
درس پنجم: حل عددی معادلات دیفرانسیل معمولی
...
برای توضیحات بیشتر و تهیه این آموزش لطفا به لینک زیر مراجعه بفرمائید:
http://faradars.org/courses/fvmth102
Variational이라는 단어로는 아무것도 안떠오릅니다.
그래서, '꿩 대신 닭'이라고 표현해 봤습니다.
초반 독자적인 그림을 통해 개념잡기가 쉬워요.
설명부분은 초록색으로 표시했습니다.
확률변수(random variable)부터 막히면, 아래 블로그 글을 읽어 보세요.
https://blog.naver.com/nonezerok/221428251262
Drift analysis is among the most powerful theoretical tools available for estimating the optimisation time of meta-heuristics. Informally, it shows how the challenging problem of predicting the long-term behaviour of a meta-heuristic can be reduced to the often trivial problem of describing how the state of the heuristic changes during one iteration.
Drift analysis has dramatically simplified the analysis of meta-heuristics. Many of the most important results about the optimisation time of meta-heuristics were obtained with the help of drift analysis.
This tutorial gives a gentle, yet comprehensive, introduction to drift analysis, assuming only basic knowledge of probability theory. We approach the area by examining a few simple drift theorems that are both straightforward to apply, and that yield useful bounds on the expected optimisation time. We then turn to more sophisticated drift theorems that, while needing stronger conditions, allow us to make very precise statements about the success probability of meta-heuristics. Finally, we show how to investigate complex evolutionary algorithms with the aid of a new population-drift theorem that was discovered recently.
This slide introduces transformer-xl which is the base paper for xl-net. You can understand what is the major contribution of this paper using this slide. This slide also explains the transformer for comparing differences between transformer and transformer-xl. Happy NLP!
محاسبات عددی علم و هنر محاسبه است. محاسبات عددی (یا آنالیز عددی) به مطالعه ی روش ها و الگوریتم هایی گفته می شود که تقریب های عددی (در مقابل جواب های تحلیلی) را برای مسائل ریاضی بکار می برند. محاسبات عددی با اعمال شیوه های تقریبی محاسباتی به حل مسائلی از ریاضیات پیوسته می پردازد که به روش تحلیلی قابل حل نبوده و یا به سختی قابل حل تحلیلی هستند.
سرفصل هایی که در این آموزش به آن پرداخته شده است:
درس اول: خطاها و اشتباهات
درس دوم: حل دستگاه های معادلات خطی
درس سوم: درون یابی و برازش
درس چهارم: مشتق گیری و انتگرال گیری عددی
درس پنجم: حل عددی معادلات دیفرانسیل معمولی
...
برای توضیحات بیشتر و تهیه این آموزش لطفا به لینک زیر مراجعه بفرمائید:
http://faradars.org/courses/fvmth102
Variational이라는 단어로는 아무것도 안떠오릅니다.
그래서, '꿩 대신 닭'이라고 표현해 봤습니다.
초반 독자적인 그림을 통해 개념잡기가 쉬워요.
설명부분은 초록색으로 표시했습니다.
확률변수(random variable)부터 막히면, 아래 블로그 글을 읽어 보세요.
https://blog.naver.com/nonezerok/221428251262
Drift analysis is among the most powerful theoretical tools available for estimating the optimisation time of meta-heuristics. Informally, it shows how the challenging problem of predicting the long-term behaviour of a meta-heuristic can be reduced to the often trivial problem of describing how the state of the heuristic changes during one iteration.
Drift analysis has dramatically simplified the analysis of meta-heuristics. Many of the most important results about the optimisation time of meta-heuristics were obtained with the help of drift analysis.
This tutorial gives a gentle, yet comprehensive, introduction to drift analysis, assuming only basic knowledge of probability theory. We approach the area by examining a few simple drift theorems that are both straightforward to apply, and that yield useful bounds on the expected optimisation time. We then turn to more sophisticated drift theorems that, while needing stronger conditions, allow us to make very precise statements about the success probability of meta-heuristics. Finally, we show how to investigate complex evolutionary algorithms with the aid of a new population-drift theorem that was discovered recently.
This slide introduces transformer-xl which is the base paper for xl-net. You can understand what is the major contribution of this paper using this slide. This slide also explains the transformer for comparing differences between transformer and transformer-xl. Happy NLP!
This slide described about Deep sarsa, Deep Q-learning, and DQN, and used for Reinforcement Learning study group's lecture, where is belonged to Korea Artificial Intelligence Laboratory.
This slide described about Deep sarsa, Deep Q-learning, and DQN, and used for Reinforcement Learning study group's lecture, where is belonged to Korea Artificial Intelligence Laboratory.
3. 가우스 소거법과 행렬
• 앞의 과정을 벡터로 나타내면,
2 1 1 5
4 −6 0 −2
−2 7 2 9
2 1 1 5
0 −8 −2 −12
0 8 3 14
2 1 1 5
0 −8 −2 −12
0 0 1 2
• 과정 중에 Pivot 자리에 0이 생기면, 아래 쪽의 0이 아닌 행과 자리를 바꿀 수 있고, 이를
Pivoting이라고 한다.
Upper Triangular Matrix : U
𝑢 + 𝑣 + 𝑤 = 𝑎
2𝑢 + 2𝑣 + 5𝑤 = 𝑏
4𝑢 + 6𝑣 + 8𝑤 = 𝑐
𝑢 + 𝑣 + 𝑤 = 𝑎
3𝑤 = 𝑏 − 2𝑎
2𝑣 + 4𝑤 = 𝑐 − 4𝑎
𝑢 + 𝑣 + 𝑤 = 𝑎
2𝑣 + 4𝑤 = 𝑐 − 4𝑎
3𝑤 = 𝑏 − 2𝑎
4. Singular Case와 가우스 소거법
• Singular Case : 해가 없거나, 해가 무수히 많거나
𝑢 + 𝑣 + 𝑤 = 𝑎
2𝑢 + 2𝑣 + 5𝑤 = 𝑏
4𝑢 + 4𝑣 + 8𝑤 = 𝑐
𝑢 + 𝑣 + 𝑤 = 𝑎
3𝑤 = 𝑏 − 2𝑎
4𝑤 = 𝑐 − 4𝑎
②식에서 𝑤 =
𝑏−2𝑎
3
③식에서 𝑤 =
𝑐−4𝑎
4
이기 때문에,
𝑏−2𝑎
3
=
𝑐−4𝑎
4
일 때만 해가 존재(무수히 많은 해)
그렇지 않으면 해가 존재하지 않음
Pivot 위치에 0이 있고,
Pivoting으로도 해결할 수 없다 U 모양 실패!
5. 연립방정식의 Matrix Notation
2𝑢 + 𝑣 + 𝑤 = 5
4𝑢 − 6𝑣 = −2
−2𝑢 + 7𝑣 + 2𝑤 = 9
• 앞의 내용을 행렬로 접근해보자.
“연립방정식은 결국 행렬 𝑨의 열벡터들의 Linear Combination으로
우항(𝒃)을 만들 수 있는지를 푸는 것이다.”
2 1 1
4 −6 0
−2 7 2
𝑢
𝑣
𝑤
=
5
−2
9
Coefficient Matrix
𝑢
2
4
−2
+ 𝑣
1
−6
7
+ 𝑤
1
0
2
=
5
−2
9
𝑨𝒙 = 𝒃
𝑨𝒙 is a combination
of the columns of 𝑨.