matlab 中的eps指什么（eps=2.2204e-016）

Answer 1

不是最小的数，而是系统能准确表示的浮点数的精度。
更准确的说，就是浮点数1.0和相邻的下一个系统能表示出的浮点数之间的差。

因为计算机里是二进制表示的，根据浮点数的表示法，对于双精度浮点数(double)来说，eps=2^(-52)

Answer 2

Matlab中最小的数-eps

eps=2.2204e-016
Floating-point relative accuracy
Syntax
eps
d = eps(X)
eps('double')
eps('single')

Description

eps returns the distance from 1.0 to the next largest double-precision number, that is eps = 2^(-52).
d = eps(X) is the positive distance from abs(X) to the next larger in magnitude floating point number of the same precision as X. X may be either double precision or single precision. For all X,
eps(X) = eps(-X) = eps(abs(X))

eps('double') is the same as eps or eps(1.0).
eps('single') is the same as eps(single(1.0)) or single(2^-23).
Except for denormals, if 2^E <= abs(X) < 2^(E+1), then
eps(X) = 2^(E-23) if isa(X,'single')
eps(X) = 2^(E-52) if isa(X,'double')

Replace expressions of the form
if Y < eps * ABS(X)

with
if Y < eps(X)

Examples
double precision
eps(1/2) = 2^(-53)
eps(1) = 2^(-52)
eps(2) = 2^(-51)
eps(realmax) = 2^971
eps(0) = 2^(-1074)
if(abs(x)) <= realmin, eps(x) = 2^(-1074)
eps(Inf) = NaN
eps(NaN) = NaN
single precision
eps(single(1/2)) = 2^(-24)
eps(single(1)) = 2^(-23)
eps(single(2)) = 2^(-22)
eps(realmax('single')) = 2^104
eps(single(0)) = 2^(-149)
if(abs(x)) <= realmin('single'), eps(x) = 2^(-149)
eps(single(Inf)) = single(NaN)
eps(single(NaN)) = single(NaN)

See Also

realmax, realmin

eomday eq
? 1994-2005 The MathWorks, Inc. ? Terms of Use ? Patents ? Trademarks

Answer 3

Matlab中最小的数-eps
eps=2.2204e-016
Floating-point
relative
accuracy
Syntax
eps
d
=
eps(X)
eps('double')
eps('single')
Description
eps
returns
the
distance
from
1.0
to
the
next
largest
double-precision
number,
that
is
eps
=
2^(-52).
d
=
eps(X)
is
the
positive
distance
from
abs(X)
to
the
next
larger
in
magnitude
floating
point
number
of
the
same
precision
as
X.
X
may
be
either
double
precision
or
single
precision.
For
all
X,
eps(X)
=
eps(-X)
=
eps(abs(X))
eps('double')
is
the
same
as
eps
or
eps(1.0).
eps('single')
is
the
same
as
eps(single(1.0))
or
single(2^-23).
Except
for
denormals,
if
2^E
<=
abs(X)
<
2^(E+1),
then
eps(X)
=
2^(E-23)
if
isa(X,'single')
eps(X)
=
2^(E-52)
if
isa(X,'double')
Replace
expressions
of
the
form
if
Y
<
eps
*
ABS(X)
with
if
Y
<
eps(X)
Examples
double
precision
eps(1/2)
=
2^(-53)
eps(1)
=
2^(-52)
eps(2)
=
2^(-51)
eps(realmax)
=
2^971
eps(0)
=
2^(-1074)
if(abs(x))
<=
realmin,
eps(x)
=
2^(-1074)
eps(Inf)
=
NaN
eps(NaN)
=
NaN
single
precision
eps(single(1/2))
=
2^(-24)
eps(single(1))
=
2^(-23)
eps(single(2))
=
2^(-22)
eps(realmax('single'))
=
2^104
eps(single(0))
=
2^(-149)
if(abs(x))
<=
realmin('single'),
eps(x)
=
2^(-149)
eps(single(Inf))
=
single(NaN)
eps(single(NaN))
=
single(NaN)
See
Also
realmax,
realmin
eomday
eq
?
1994-2005
The
MathWorks,
Inc.
?
Terms
of
Use
?
Patents
?
Trademarks

Answer 4

机械零阈值

Answer 5

常数