誤差傳播

y=f(x)

x

dx

dy

dy/y

x=f(u,v,...)

x^_

s_x^2

=

1/(N-1)sum_(i=1)^(N)(x_i-x^_)^2

=

s_u^2

=

1/(N-1)sum_(i=1)^(N)(u_i-u^_)^2

s_v^2

=

1/(N-1)sum_(i=1)^(N)(v_i-v^_)^2

s_(uv)

=

1/(N-1)sum_(i=1)^(N)(u_i-u^_)(v_i-v^_)

s_(ii)=s_i^2

u

v

s_(uv)=0

x=au+/-bv

partialx/partialu=a

partialx/partialv=+/-b

x=+/-au/v

partialx/partialu=+/-a/v

partialx/partialv=∓au/v^2

x^2

a=e

x=aln(+/-bu)

partialx/partialu=a(+/-b)/(+/-bu)=a/u

x=+/-auv

partialx/partialu=+/-av

partialx/partialv=+/-au

((s_x)/x)^2

=

(a^2v^2)/(a^2u^2v^2)s_u^2+(a^2u^2)/(a^2u^2v^2)s_v^2+(2a^2uv)/(a^2u^2v^2)s_(uv)

=

((s_u)/u)^2+((s_v)/v)^2+2((s_(uv))/(uv)).

x=au^(+/-b)

partialx/partialu=+/-abu^(+/-b-1)=+/-bx/u