请教：高维数值积分# Computation - 科学计算
c*r
1 楼
我想求一个m维数值积分，
F(x_1,...,x_m;n)= \int_{y_i>=x_i, \sum y_i=n} f(y_1,...,y_m;n) dy_1 ...dy_m
x_i>=0, n>0
应该怎么求？
多谢。
F(x_1,...,x_m;n)= \int_{y_i>=x_i, \sum y_i=n} f(y_1,...,y_m;n) dy_1 ...dy_m
x_i>=0, n>0
应该怎么求？
多谢。
i*n
2 楼
蒙特卡罗
【在 c****r 的大作中提到】
: 我想求一个m维数值积分，
: F(x_1,...,x_m;n)= \int_{y_i>=x_i, \sum y_i=n} f(y_1,...,y_m;n) dy_1 ...dy_m
: x_i>=0, n>0
: 应该怎么求？
: 多谢。
c*e
3 楼
gaussian quadrature
我以前做过4维的,都一样套就可以了
【在 c****r 的大作中提到】
: 我想求一个m维数值积分，
: F(x_1,...,x_m;n)= \int_{y_i>=x_i, \sum y_i=n} f(y_1,...,y_m;n) dy_1 ...dy_m
: x_i>=0, n>0
: 应该怎么求？
: 多谢。
我以前做过4维的,都一样套就可以了
【在 c****r 的大作中提到】
: 我想求一个m维数值积分，
: F(x_1,...,x_m;n)= \int_{y_i>=x_i, \sum y_i=n} f(y_1,...,y_m;n) dy_1 ...dy_m
: x_i>=0, n>0
: 应该怎么求？
: 多谢。
w*d
4 楼
If the dimension is really high, Monte Carlo is the best choice.
【在 i*******n 的大作中提到】
:
: 蒙特卡罗
n*s
5 楼
and probably the only choice
【在 w**d 的大作中提到】
:
: If the dimension is really high, Monte Carlo is the best choice.
【在 w**d 的大作中提到】
:
: If the dimension is really high, Monte Carlo is the best choice.
w*d
6 楼
Is there any good answer to the curse of dimension?
【在 n*s 的大作中提到】
: and probably the only choice
n*s
7 楼
the error for MC is
O (N ^ {-1/2})
for ordinary numerical integration, the error is
O (N ^ {-a/d})
d is the dimention of the problem, a is related to the algorithm
【在 w**d 的大作中提到】
:
: Is there any good answer to the curse of dimension?
O (N ^ {-1/2})
for ordinary numerical integration, the error is
O (N ^ {-a/d})
d is the dimention of the problem, a is related to the algorithm
【在 w**d 的大作中提到】
:
: Is there any good answer to the curse of dimension?
c*r
8 楼
Sounds interesting.
What is MC and N?
Is it an abosolute error or relative error?
【在 n*s 的大作中提到】
: the error for MC is
: O (N ^ {-1/2})
: for ordinary numerical integration, the error is
: O (N ^ {-a/d})
: d is the dimention of the problem, a is related to the algorithm
What is MC and N?
Is it an abosolute error or relative error?
【在 n*s 的大作中提到】
: the error for MC is
: O (N ^ {-1/2})
: for ordinary numerical integration, the error is
: O (N ^ {-a/d})
: d is the dimention of the problem, a is related to the algorithm
n*s
9 楼
MC is Monte Carlo
N is the # of intervals into which is original intergration interval is divide
【在 c****r 的大作中提到】
: Sounds interesting.
: What is MC and N?
: Is it an abosolute error or relative error?
N is the # of intervals into which is original intergration interval is divide
【在 c****r 的大作中提到】
: Sounds interesting.
: What is MC and N?
: Is it an abosolute error or relative error?
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