Changes between Version 9 and Version 10 of PolynomialExpansion


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Timestamp:
01/26/16 11:24:18 (10 years ago)
Author:
sili
Comment:

--

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  • PolynomialExpansion

    v9 v10  
    11
    22A = x0, x1   b = x3[2]
    3       x1, x2
     3    x1, x2
    44
    55Step 1: r = b - Ax
    66  r[0] = x3[0]
    7 
    87  r[1] = x3[1]
    98
    … …  
    1211
    1312Step 3: r[i] = r - alpha * A[i][j] * p[j]
    14   r[0] = (-1*((X3[1]^3)*X1)-1*((X3[1]^2)*X3[0]*X0)+(X3[1]^2)*X3[0]*X2+X3[1]*(X3[0]^2)*X1) / ((X3[1]^2)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2)*X0)
     13  r[0] = (-X3[1]*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)
    1514
    16   r[1] = ((X3[1]^2)*X3[0]*X1+X3[1]*(X3[0]^2)*X0-1*(X3[1]*(X3[0]^2)*X2)-1*((X3[0]^3)*X1)) / ((X3[1]^2)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2)*X0)
    17 
    18   r[0] = (X3[0]^2^ + X3[1]^2^) / (X0 X3[0]^2^ + 2 X1 X3[0] X3[1] + X2 X3[1]^2^)
     15  r[1] = (X3[0]*(-X1*X3[0]^2^ + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2^)) / (X0*X3[0]^2^ + 2*X1*X3[0]*X3[1] + X2*X3[1]^2^)
    1916
    2017Step 4: x[i] = x + alpha*p[i]
    21   x[0] = ((X3[1]^2)*X3[0]+X3[0]^3) / ((X3[1]^2)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2)*X0)
     18  x[0] = (X3[0]*(X3[0]^2 + X3[1]^2)) / (X0*X3[0]^2 + 2*X1*X3[0]*X3[1] + X2*X3[1]^2)
    2219
    23   x[1] = (X3[1]^3 + X3[1]*(X3[0]^2)) / ((X3[1]^2)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2)*X0)
     20  x[1] = (X3[1]*(X3[0]^2 + X3[1]^2)) / (X0*X3[0]^2 + 2*X1*X3[0]*X3[1] + X2*X3[1]^2)
    2421
    2522Step 5: beta = (rk[i]*rk[i]) / (r[i]*r[i])
    26   beta = ((X3[1]^6)*(X1^2)+2*((X3[1]^5)*X3[0]*X0*X1)-2*((X3[1]^5)*X3[0]*X1*X2)+(X3[1]^4)*(X3[0]^2)*(X0^2)-2*((X3[1]^4)*(X3[0]^2)*X0*X2)-1*((X3[1]^4)*(X3[0]^2)*(X1^2))+(X3[1]^4)*(X3[0]^2)*(X2^2)+(X3[1]^2)*(X3[0]^4)*(X0^2)-2*((X3[1]^2)*(X3[0]^4)*X0*X2)-1*((X3[1]^2)*(X3[0]^4)*(X1^2))+(X3[1]^2)*(X3[0]^4)*(X2^2)-2*(X3[1]*(X3[0]^5)*X0*X1)+2*(X3[1]*(X3[0]^5)*X1*X2)+(X3[0]^6)*(X1^2))/((X3[1]^6)*(X2^2)+4*((X3[1]^5)*X3[0]*X1*X2)+2*((X3[1]^4)*(X3[0]^2)*X0*X2)+4*((X3[1]^4)*(X3[0]^2)*(X1^2))+(X3[1]^4)*(X3[0]^2)*(X2^2)+4*((X3[1]^3)*(X3[0]^3)*X0*X1)+4*((X3[1]^3)*(X3[0]^3)*X1*X2)+(X3[1]^2)*(X3[0]^4)*(X0^2)+2*((X3[1]^2)*(X3[0]^4)*X0*X2)+4*((X3[1]^2)*(X3[0]^4)*(X1^2))+4*(X3[1]*(X3[0]^5)*X0*X1)+(X3[0]^6)*(X0^2))
     23  beta = (X1*X3[0]^2 - X0*X3[0]*X3[1] + X2*X3[0]*X3[1] - X1*X3[1]^2)^2 / (X0*X3[0]^2 + 2*X1*X3[0]*X3[1] + X2*X3[1]^2)^2
    2724
    2825Step 6: p[i] = rk[i] +beta * p
    29   p[0] = (-1*((X3[1]^7)*X1*X2)-1*((X3[1]^6)*X3[0]*X0*X2)-1*((X3[1]^6)*X3[0]*(X1^2))+(X3[1]^6)*X3[0]*(X2^2)-1*((X3[1]^5)*(X3[0]^2)*X0*X1)-2*((X3[1]^4)*(X3[0]^3)*X0*X2)-1*((X3[1]^4)*(X3[0]^3)*(X1^2))+2*((X3[1]^4)*(X3[0]^3)*(X2^2))-2*((X3[1]^3)*(X3[0]^4)*X0*X1)+3*((X3[1]^3)*(X3[0]^4)*X1*X2)-1*((X3[1]^2)*(X3[0]^5)*X0*X2)+(X3[1]^2)*(X3[0]^5)*(X1^2)+(X3[1]^2)*(X3[0]^5)*(X2^2)-1*(X3[1]*(X3[0]^6)*X0*X1)+2*(X3[1]*(X3[0]^6)*X1*X2)+(X3[0]^7)*(X1^2))/((X3[1]^6)*(X2^2)+4*((X3[1]^5)*X3[0]*X1*X2)+2*((X3[1]^4)*(X3[0]^2)*X0*X2)+4*((X3[1]^4)*(X3[0]^2)*(X1^2))+(X3[1]^4)*(X3[0]^2)*(X2^2)+4*((X3[1]^3)*(X3[0]^3)*X0*X1)+4*((X3[1]^3)*(X3[0]^3)*X1*X2)+(X3[1]^2)*(X3[0]^4)*(X0^2)+2*((X3[1]^2)*(X3[0]^4)*X0*X2)+4*((X3[1]^2)*(X3[0]^4)*(X1^2))+4*(X3[1]*(X3[0]^5)*X0*X1)+(X3[0]^6)*(X0^2))
    30  
    31   p[1] = ((X3[1]^7)*(X1^2)+2*((X3[1]^6)*X3[0]*X0*X1)-1*((X3[1]^6)*X3[0]*X1*X2)+(X3[1]^5)*(X3[0]^2)*(X0^2)-1*((X3[1]^5)*(X3[0]^2)*X0*X2)+(X3[1]^5)*(X3[0]^2)*(X1^2)+3*((X3[1]^4)*(X3[0]^3)*X0*X1)-2*((X3[1]^4)*(X3[0]^3)*X1*X2)+2*((X3[1]^3)*(X3[0]^4)*(X0^2))-2*((X3[1]^3)*(X3[0]^4)*X0*X2)-1*((X3[1]^3)*(X3[0]^4)*(X1^2))-1*((X3[1]^2)*(X3[0]^5)*X1*X2)+X3[1]*(X3[0]^6)*(X0^2)-1*(X3[1]*(X3[0]^6)*X0*X2)-1*(X3[1]*(X3[0]^6)*(X1^2))-1*((X3[0]^7)*X0*X1))/((X3[1]^6)*(X2^2)+4*((X3[1]^5)*X3[0]*X1*X2)+2*((X3[1]^4)*(X3[0]^2)*X0*X2)+4*((X3[1]^4)*(X3[0]^2)*(X1^2))+(X3[1]^4)*(X3[0]^2)*(X2^2)+4*((X3[1]^3)*(X3[0]^3)*X0*X1)+4*((X3[1]^3)*(X3[0]^3)*X1*X2)+(X3[1]^2)*(X3[0]^4)*(X0^2)+2*((X3[1]^2)*(X3[0]^4)*X0*X2)+4*((X3[1]^2)*(X3[0]^4)*(X1^2))+4*(X3[1]*(X3[0]^5)*X0*X1)+(X3[0]^6)*(X0^2))
     26  p[0] = (-1)*((X1*X3[0] + X2*X3[1])*(X3[0]^2 + X3[1]^2)*(-X1*X3[0]^2 + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2)) / (X0*X3[0]^2 + 2*X1*X3[0]*X3[1] + X2*X3[1]^2)^2
     27
     28  p[1] = ((X0*X3[0] + X1*X3[1])*(X3[0]^2 + X3[1]^2)*(-X1*X3[0]^2 + X0*X3[0]*X3[1] - X2*X3[0]*X3[1] + X1*X3[1]^2)) / (X0*X3[0]^2 + 2*X1*X3[0]*X3[1] + X2*X3[1]^2)^2
    3229
    3330Step 7: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
    34   alpha =
     31  alpha = (X0*X3[0]^2 + 2*X1*X3[0]*X3[1] + X2*X3[1]^2) / ((-X1^2 + X0 X2) (X3[0]^2 + X3[1]^2))
    3532
    3633Step 8: r[i] = r - alpha * A[i][j] * p[j]
    3734  r[0] = 0
    38 
    3935  r[1] = 0
    4036
    4137Step 9: x[i] = x + alpha*p[i]
    42   x[0] =
    43 
    44   x[1] =
     38  x[0] = (X2*X3[0] - X1*X3[1]) / (X0*X2 - X1^2)
     39  x[1] = (-X1 X3[0] + X0 X3[1]) / (X0*X2 - X1^2)
    4540
    4641END