Changes between Initial Version and Version 1 of PolynomialExpansion


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Timestamp:
01/25/16 23:54:27 (10 years ago)
Author:
sili
Comment:

--

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  • PolynomialExpansion

    v1 v1  
     1
     2A = x0, x1   b = x3[2]
     3    x1, x2
     4
     5Step 1: r = b - Ax
     6  r[0] = x3[0]
     7  r[1] = x3[1]
     8
     9Step 2: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
     10  alpha = (X3[0]^2+X3[1]^2) / ((X3[1]^2)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2)*X0)
     11
     12Step 3: r[i] = r - alpha * A[i][j] * p[j]
     13  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)
     14  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)
     15
     16Step 4: x[i] = x + alpha*p[i]
     17  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[1] = (X3[1]^3+X3[1]*(X3[0]^2)) / ((X3[1]^2)*X2+2*(X3[1]*X3[0]*X1)+(X3[0]^2)*X0)
     19
     20Step 5: beta = (rk[i]*rk[i]) / (r[i]*r[i])
     21  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))
     22
     23Step 6: p[i] = rk[i] +beta * p
     24  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))
     25  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
     27Step 7: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
     28  alpha =
     29
     30Step 8: r[i] = r - alpha * A[i][j] * p[j]
     31  r[0] = 0
     32  r[1] = 0
     33
     34Step 9: x[i] = x + alpha*p[i]
     35  x[0] =
     36  x[1] =
     37
     38END