:⸴Է(߸Իع)

ʽ:
[a,R,er]=PluralSolveEquation(x1,x2,,xn,y,t)
[a,R,er]=PluralSolveEquation(x1,x2,,xn,y)

x1,x2,,xn:Ϊyһ,Ϊ12ľ,еһбʾʵ,ڶбʾ
y:Ϊx1һ,Ϊ12ľ,еһбʾʵ,ڶбʾ
t:ֵ,ΪʱֻΪΪ1ľ,ÿԪطֱӦxϵaΪ1ʱʾֵΪΪʵ

a:õĽ,зصĵһΪʵ,ڶΪ
R:Rϵ
er:ľ


ԭ:

1ôһ,֪һ x1,x2,,xn,y ¹ϵʽ

    y = a1*x1 + a2*x2 +  + an*xn

2һ x1,x2,,xn,y,a1,a2,,anһЩΪ,ڶ.

3ڲȵ{SolveEquationLSM2<\SolveEquationLSM2>},ʧ,ٵ{SolveEquationGauss<\SolveEquationGauss>}⡣ڼRϵʱú{DataSimilarityR<\DataSimilarityR>}м㡣

ע:

1ΪԷ,ʵҲɼԹ滮(ԭһ)

2ָϵΪʵ,,ϸʾ

:
//4,x1,x2,x3,y ֻx3Ϊʵ y = a1*x1 + a2*x2 + a3*x3еĸϵa1,a2,a3׼ȷ a1 = 1- 2i ; a2 = 3 ; a3 = -3 + 2i
x1 =
[ 15.0000000000000    3.00000000000000
  16.0000000000000    5.00000000000000
  3.00000000000000    19.0000000000000
  16.0000000000000    12.0000000000000
  8.00000000000000    1.00000000000000 ]
x2 =
[ 10.0000000000000    24.0000000000000
  24.0000000000000    16.0000000000000
  18.0000000000000    15.0000000000000
  19.0000000000000    15.0000000000000
  1.00000000000000    15.0000000000000 ]
x3 =
[ 9.00000000000000
  9.00000000000000
  1.00000000000000
  1.00000000000000
  14.0000000000000 ]
y =
[ 24.0000000000000    63.0000000000000
  71.0000000000000    39.0000000000000
  92.0000000000000    60.0000000000000
  94.0000000000000    27.0000000000000
 -29.0000000000000    58.0000000000000 ]

[a,r,er]=PluralSolveEquation(x1,x2,x3,y)//ϵͳѾ4,سִбԵõa,a1=0.99999999999973-2.00000000000033i,a2=3.00000000000005+3.2612801348E-13i,a3=-2.99999999999912+2.00000000000009i
a =
[ 0.99999999999973   -2.00000000000033
  3.00000000000005    3.2612801348E-13
 -2.99999999999912    2.00000000000009 ]
r =
[ 1.00000000000000 ]
er =
[ 6.7738110157E-23 ]

(2)
//ָϵa1,a3Ϊ,a2Ϊʵ,tеԪζӦa1,a2,a3Ϊ1߳ΪΪʵ

t=[1 0 1];[a,r,er]=PluralSolveEquation(x1,x2,x3,y,t)//سõ½,ɷa2һΪ0
a =
[ 1.00000000000002   -1.99999999999991
  2.99999999999998    0.00000000000000
 -2.99999999999999    2.00000000000000 ]
r =
[ 1.00000000000000 ]
er =
[ 9.4323656675E-24 ]

(3)
//ֱӱ任һ,ϵΪʵ,Ч
t=[0 0 0];[a,r,er]=PluralSolveEquation(x1,x2,x3,y,t)//سõ½,a1=0.48042149802710,a2=3.37880786320421,a3=-2.13390894820837,Ǵrϵ0.85509179939612,ǲв3251.63134541989 ,ĽԱȲ໹Ǻܴ
a =
[ 0.48042149802710    0.00000000000000
  3.37880786320421    0.00000000000000
 -2.13390894820837    0.00000000000000 ]
r =
[ 0.85509179939612 ]
er =
[ 3251.63134541989 ]

(4)
//ҪϵϵֻҪ,a1ֵΪ m*imҪ,ʱ,ݸ,ɽa1Ӧϵ,Ϊx1,ôx1־ȡ෴ֵ(0ȥ),Ȼʵֻ,ָa1Ϊʵַ⼴.


//By 2014/12/01 11:00:00