# Least Squares Fitting

## 전체 글

(1)

(2)

(3)

(4)
(5)
(6)
(7)
(8)

(9)

(10)

i

i

i

(11)
(12)

i

i

(13)

i

i

### Total Error:

E = 1 N Ni=1 yi− axi− b

(14)

i

i

### Total Error:

E = 1 N Ni=1 yi− axi− b E = N i=1 yi − axi− b : const. N

(15)

i

i

### Total Error:

E = 1 N Ni=1 yi− axi− b E = N i=1 yi − axi− b : const. N E = Ni=1 (yi − axi− b)2

(16)

i

i

### Total Error:

E = 1 N Ni=1 yi− axi− b E = N i=1 yi − axi− b : const. N argmin a,b E

E = N

i=1 (yi

(17)

i

i

### Total Error:

E = 1 N Ni=1 yi− axi− b E = N i=1 yi − axi− b : const. N argmin a,b E

### = 0

E = N i=1 (yi − axi− b)2 ∂E ∂a = 2 Ni=1 (yi − axi− b) ⋅ (−xi) = 0 ∂E ∂b = 2 Ni=1 (yi − axi− b) ⋅ (−1) = 0

(18)

### Mathematical Formulation

∂E ∂a = 2 Ni=1 (yi − axi− b) ⋅ (−xi) = 0 ∂E ∂b = 2 Ni=1 (yi − axi− b) ⋅ (−1) = 0 (− Ni=1 xiyi)+ a( Ni=1 x2 i )+ b( Ni=1 xi) = 0 (− Ni=1 yi )+ a( Ni=1 xi )+ bN = 0 a(N i=1 x2 i )+ b( Ni=1 xi) = ( Ni=1 xiyi) a ( Ni=1 xi )+ bN = ( Ni=1 yi ) ∑Ni=1x2 iNi=1xiNi=1xi N

### b]

= ∑ N i=1xiyiNi=1yi

(19)

### Mathematical Formulation

∂E ∂a = 2 Ni=1 (yi − axi− b) ⋅ (−xi) = 0 ∂E ∂b = 2 Ni=1 (yi − axi− b) ⋅ (−1) = 0 (− Ni=1 xiyi)+ a( Ni=1 x2 i )+ b( Ni=1 xi) = 0 (− Ni=1 yi )+ a( Ni=1 xi )+ bN = 0 a(N i=1 x2 i )+ b( Ni=1 xi) = ( Ni=1 xiyi) a ( Ni=1 xi )+ bN = ( Ni=1 yi ) ∑Ni=1x2 iNi=1xiNi=1xi N

### b]

= ∑ N i=1xiyiNi=1yi

(20)

(21)

Updating...

관련 주제 :