Changes between Version 31 and Version 32 of PolynomialExpansion


Ignore:
Timestamp:
01/26/16 16:20:00 (10 years ago)
Author:
sili
Comment:

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  • PolynomialExpansion

    v31 v32  
    11
    2 A = {{a,,0,,, a,,1,,}, {a,,1,,, a,,2,,}},  b = {b,,0,,, b,,1,,}, x = {0, 0}
     2A = {{a,,0,,, a,,1,,}, {a,,1,,, a,,2,,}},  b = {b,,0,,, b,,1,,}, x,,0,, = {0, 0}
    33
    44
    … …  
    1111
    1212Step 2: alpha,,0,, = <r,,0,,, r,,0,,> / <p,,0,,, Ap,,0,,>
    13   <p, Ap> = a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^
     13  <p,,0,,, Ap,,0,,> = a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^
    1414
    1515  alpha,,0,, = (b,,0,,^2^+b,,1,,^2^) / ((b,,1,,^2^)*a,,2,,+2*(b,,1,,*b,,0,,*a,,1,,)+(b,,0,,^2^)*a,,0,,)
    … …  
    2020  r[1] = (b,,0,,*(-a,,1,,*b,,0,,^2^ + a,,0,,*b,,0,,*b,,1,, - a,,2,,*b,,0,,*b,,1,, + a,,1,,*b,,1,,^2^)) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)
    2121
    22 Step 4: x[i] = x + alpha*p
     22Step 4: x,,1,, = x,,0,, + alpha*p,,0,,
    2323  x[0] = (b,,0,,*(b,,0,,^2^ + b,,1,,^2^)) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)
    2424
    2525  x[1] = (b,,1,,*(b,,0,,^2^ + b,,1,,^2^)) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)
    2626
    27 Step 5: beta = rsnew / rsold = <r,,k+1,,, r,,k+1,,> / <r,,k,,, r,,k,,>
     27Step 5: beta = rsnew / rsold = <r,,1,,, r,,1,,> / <r,,0,,, r,,0,,>
    2828  rsnew = ((b,,0,,^2^ + b,,1,,^2^)*(-a,,1,,*b,,0,,^2^ + a,,0,,*b,,0,,*b,,1,, - a,,2,,*b,,0,,*b,,1,, + a,,1,,*b,,1,,^2^)^2^) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)^2^
    2929
    3030  beta = (a,,1,,*b,,0,,^2^ - a,,0,,*b,,0,,*b,,1,, + a,,2,,*b,,0,,*b,,1,, - a,,1,,*b,,1,,^2^)^2^ / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)^2^
    3131
    32 Step 6: p[i] = r[i] +beta * p
     32Step 6: p,,1,, = r,,1,, +beta * p,,0,,
    3333  p[0] = (-1)*((a,,1,,*b,,0,, + a,,2,,*b,,1,,)*(b,,0,,^2^ + b,,1,,^2^)*(-a,,1,,*b,,0,,^2^ + a,,0,,*b,,0,,*b,,1,, - a,,2,,*b,,0,,*b,,1,, + a,,1,,*b,,1,,^2^)) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)^2^
    3434
    3535  p[1] = ((a,,0,,*b,,0,, + a,,1,,*b,,1,,)*(b,,0,,^2^ + b,,1,,^2^)*(-a,,1,,*b,,0,,^2^ + a,,0,,*b,,0,,*b,,1,, - a,,2,,*b,,0,,*b,,1,, + a,,1,,*b,,1,,^2^)) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)^2^
    3636
    37 Step 7: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
    38   p[i]*(A[i][j]*p[j]) = ((-a,,1,,^2^ + a,,0,,*a,,2,,)*(b,,0,,^2^ + b,,1,,^2^)^2^*(-a,,1,,*b,,0,,^2^ + a,,0,,*b,,0,,*b,,1,, - a,,2,,*b,,0,,*b,,1,, + a,,1,,*b,,1,,^2^)^2^) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)^3^
     37Step 7: alpha,,1,, = <r,,1,,, r,,1,,> / <p,,1,,, Ap,,1,,>
     38  <p,,1,,, Ap,,1,,> = ((-a,,1,,^2^ + a,,0,,*a,,2,,)*(b,,0,,^2^ + b,,1,,^2^)^2^*(-a,,1,,*b,,0,,^2^ + a,,0,,*b,,0,,*b,,1,, - a,,2,,*b,,0,,*b,,1,, + a,,1,,*b,,1,,^2^)^2^) / (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^)^3^
    3939
    40   alpha = (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^) / ((-a,,1,,^2^ + a,,0,,*a,,2,,) (b,,0,,^2^ + b,,1,,^2^))
     40  alpha,,1,, = (a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^) / ((-a,,1,,^2^ + a,,0,,*a,,2,,) (b,,0,,^2^ + b,,1,,^2^))
    4141
    42 Step 8: r[i] = r - alpha * A[i][j] * p[j]
     42Step 8: r,,2,, = r,,1,, - alpha,,1,, * Ap,,1,,
    4343  r[0] = 0
    4444
    4545  r[1] = 0
    4646
    47 Step 9: x[i] = x + alpha*p[i]
     47Step 9: x,,2,, = x,,1,, + alpha,,1,,*p,,1,,
    4848  x[0] = (a,,2,,*b,,0,, - a,,1,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^)
    4949