r*******y
发帖数: 1081 | 1 -1 <= x1 < x2 < x3 <= 1 and -1 <= x <= 1
find x1, x2, x3 such that the max of |(x-x1)(x-x2)(x-x3)| when -1 <= x <= 1
is as small as possible.
Thanks. |
b******v
发帖数: 1493 | 2 Chebyshev polynomials吧
解是f(x)=1/4 T_3(x) = x^3-0.75*x=x(x+sqrt(3)/2)(x-sqrt(3)/2)
从而x1 = -sqrt(3)/2, x2 = 0, x3 = sqrt(3)/2
绝对值最大值是1/4
1
【在 r*******y 的大作中提到】
: -1 <= x1 < x2 < x3 <= 1 and -1 <= x <= 1
: find x1, x2, x3 such that the max of |(x-x1)(x-x2)(x-x3)| when -1 <= x <= 1
: is as small as possible.
: Thanks.
|
r*******y
发帖数: 1081 | 3 any easy proof or link to show that this solution is just T_3(x)? Thanks.
【在 b******v 的大作中提到】
: Chebyshev polynomials吧
: 解是f(x)=1/4 T_3(x) = x^3-0.75*x=x(x+sqrt(3)/2)(x-sqrt(3)/2)
: 从而x1 = -sqrt(3)/2, x2 = 0, x3 = sqrt(3)/2
: 绝对值最大值是1/4
:
: 1
|
b******v
发帖数: 1493 | 4 http://en.wikipedia.org/wiki/Chebyshev_polynomials#Minimal_.E2.88.9E-norm
【在 r*******y 的大作中提到】
: any easy proof or link to show that this solution is just T_3(x)? Thanks.
|
r*******y
发帖数: 1081 | |
