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1 3 S - (sootg) j = j +, = + () = j E ( ) = µ ( ) = = = ( )( µ ) = E µ [ ] E () = E ( ) µ = = (3) = E ( µ ) = = = = = (4) T, At t = + ( ) C ( t) t T T µ C ( t) C( t) = E j, = j (5) (6) (3)(5)

2 T (5) T τ = ( )( C ( τ ) ) T µ dt (7) T ( t τ ) T (7) P () ( ( ) ) τ µ dτ = T C T (8) P ( ) ω f W o u w = u j+ W = L W = L (9) L U U U U = W ( t) + W( t) W( jt) C( t) = L = L j= + µ W ()

3 3 (Savtzy-Golay ) W(j) W W RC P F F = ap + AP + () Gra + ( ) ( )( ) = ( ) ( ) ( ) = ( ) ( + ) () P, ( ) = P P,, () = = ( ) () = ( ) (3) P () P () =, j (4) = j,,

4 Y + ( ) (5) = Q = a P + a P + + ap Y Q = a ( ap + app j j YP = j= J ) = (6) a P YP = (6 ) = = a = = = YP, ( ) P, () (7) Y Y, = Yu = a P () 8 j= = YP j, ( j) P, ( ) = A j= A = P ( j), P,( j) = Y P j= = A (), = W + =,,,, +, W () { } W () = 3 ( + ) 5, = W ( ) = (4 )(+ 3) /3 5

5 ( ) DATA() IW(Q) I= J-,SUM= SMOOTH() SUM=SUMDATA(JI)IW(J) J=J JQ Y SMOOTH(I)=SUM/F F I=I I=Q Y SMOOT()DATA

6 () = S() + () ( )( () S () ( E S( u) S ( ) ) () S () = () () + () () ( ) () = E[ ()] ( + j), = + j = ( ) ( ) j= () = E () () ( + j) (), + (9) () () () S () () S () ()

7 3- ()( t =,,, ) t t Z () t = () t () = Z () t µ () t Z () t () t Z () t = + ( ) C(,) t µ () t R= C ( t), C (, t) = E ( t) ( t), = j () j [ ] C(, t) = E ( t) j( t) = E ( t) E j( t ) = µ = C(, t) = E ( t) = ( t) + µ () () t z () t = (3) / S / f (3) S (3) 5 / 5...

8 S apparatus fucto/struetal fucto,c, g( ν ) f ( ν ) g( ν) = a( ν ) f( ν ν ) dν, a( ν ) dν = (4) o o o o o a( ν ) a( ν ) g( ν ) ( f ν ) (4) (4) = g( ν ) a( ν) f ( ν ν ) (5) g( ν ) = a( ν ν ) f( ν [ g ] [ a ][ f ] ) (5 ) = (6) = (6) a > a Jacob j ( + ) ( ) ( ) f = f + g a f a (7) = ( R) f f f f f f f ( r+ ) ( r) () () ( r+ ) ( r) = + + ( r+ ) () ( r+ ) = f f f Gauss-Sedel f f g a f a f ( + ) ( ) ( + ) ( ) = + j j j j a j= j= (8)

9 ( + ) f ( + f ) + Burger-Cttert ( ) ( ) τ = g ( ν) = f ( τ) a( ν τ) ( + ) ( ) ( ) f ( ν ) = f ( ν) + g( ν) g ( ν) (9) Jacob = a f ( ν ) (9) G = F. A F = F + G G = F ( A) +G (3) + F = G + A + A + + A G F G/ ( ( A) ) = = F A ( ) ( ) ( ) (3) A < ()a()

10 A a = b A = a a a b b = M + C () ( ) ν ( ν+ ) ( ν) = M + C ( ν =,, ( ν + ) ν M M ( ρ M ) (M) A=D+L+U a L = a a U a a = a b ν+ ( ν) = ajj + a D ( L U) D a ( ν+ ) ( ν) = D ( L+ U) + D b = + + b

11 D D ν+ ( ν) = ajj a + a a ( D+ L) = U + b ( ν+ ) ( ν) ( D+ L) = U + b ( ) ( ) ( ) ν+ = D ( L ν+ + U ν ) + D b ( ν + ) ( ( ν+ ) ( ν) ) = j j + j + a j< j a a a b ( ν + ) ( ( ν+ ) ( ν) ) = j + j a j< j a + (, aj a b b = ) ν ( ν + ) ( ) ( ) ν ν + + ( ) ν ω SOR(Successve Over Relaato) = ω( D+L) (-U +b) + ( ω) ( ν + ) - (ν) ( ν )

12 f ( ) f ( ) s ( ) ( ) f ( ) = s( ) + ( ) (Fourer) F( ω) = S( ω) + ( ω) (3) F( ω) = f( ) e ω d (3) s ( ), ( ) S( ω) ( ω) s ( ) ( ) S S( ω) dω/ ( ω) dω (33) F() P() S( ω) dω/ ( ω) dω (34) (33) () F() Fourer S ˆ( ) ( ) ( ) ω S= Fω Pω e d π ω (35) P()(34) S S () (35) P() p( ) = P( ω)ep( ω) π dw (36) s'( ) = f( ') p( ') d' (37).. DC o (38) F() = f ( ) e d = f ( ) d

13 g ( ) f ( ) a ( ) g ( ) = f( ') a ( ') d' (39) (39) (37) G( ω) = F( ω) A( ω) (4) f ( ) f ( ) = [ G( ω) / A( ω) ] ep( ω) d π ω (4) P( ω) = / A( ω) (4) (4) g ( ) ω ±A() G()A() G()/A() g ( ) G() (4) /A() /A() W() (4) A( ω) = A( ω) A ( ω) (43) A() f ( ) = G( ω) / A ( ω) ep( ω) dω [ ] π = f ( ') a ( ') d' (44) f ( ) ( f ) a ( ) g ( ) a ( ) A().4.4 Loretz Gauss

14 ( ) Y Y, Y Y Yˆ = P(, a, a, a ) Y a a W ( ),( ) = Q= W F Y > (45) F F F, P, P,, P F, P',, P ', P', ), P ' Pj (46) ( ) = ( ) + ( j= Pj Pj=Pj-Pj' Pj F(,P P )F j= F ' F = F ' + APj (46 ) Pj (I=) Q Q = ( Pj) F ' F ' F ' Pj W = W ( Y F ') (47) Pj P P j= = = Pj Pj ' + Pj = Pj '' ( q) P P = (48) ( q+ ) ( q) < ε (49) P P ε F Aj B F = Aj + B j= Aj 3 B

15 =3 Q Q Q dq = da + da + da a a a Q Q Q Q =,,, a a a Qa (, a,, a ) = Qa (, a,, a ) +α Q a Q = a α a ( + ) ( ) a= a ( ) ( + ) ( + ) ( + ) ( ) ( ) ( ) Qa (, a,, a ) = Qa (, a,, a ) α Q Q= S Q( A+B) = A Sj Sj Sj S j Q( A+B) = Sj + B + BSj a j= a a a a a Q Q( A+B ) = Q( A ) + B = Q( ) + B S a A S j Cj =, =, j = a T CCB+CS = T T - T B=-(C C) C S T CC j j S a j ( B) f ( ) = Aep( ) + C D

16 ( ) (regular) 3 elder Mead ( ) ) f( ) = a ƒ, = + ) s f( ) = a ƒ, s 3) f( ) = ƒ, = + l ( ) ( ) 4) G G = ) (refrecto) r =( α ) + G α r r G G ) (epaso) r ( ) = γ + γ, γ > e r G, γ 3) (cotracto) c ( ) = β + β,< β < c G

17 ),,, ) r 3) ( ) ( ) ( s r ) S G ƒ ƒ ƒ r ) ƒ <ƒ 4) ( ) ( r ) ( ) ( r ) r G ƒ >ƒ e e ( ) ( ƒ ƒ e r r ) ) ƒ > ƒ > ƒ s 5) ( ) ( ) ( r ) r ( ) ( ) ƒ ƒ r c ƒ ( ) ƒ( ( ) ( c ) ) ) ƒ ƒ c ) = ( + ), c

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