Changes between Version 35 and Version 36 of PolynomialExpansion


Ignore:
Timestamp:
01/26/16 19:13:27 (10 years ago)
Author:
sili
Comment:

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Modified

  • PolynomialExpansion

    v35 v36  
    99
    1010Step 2: alpha,,0,, = <r,,0,,, r,,0,,> / <p,,0,,, Ap,,0,,>
    11   <p,,0,,, Ap,,0,,> = b,,0,,*(a,,0,,*b,,0,, + a,,1,,*b,,1,,) + b,,1,,*(a,,1,,*b,,0,, + a,,2,,*b,,1,,)
     11  <p,,0,,, Ap,,0,,> = b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)
    1212
    13   alpha,,0,, = (b,,0,,^2^+b,,1,,^2^) / b,,0,,*(a,,0,,*b,,0,, + a,,1,,*b,,1,,) + b,,1,,*(a,,1,,*b,,0,, + a,,2,,*b,,1,,)
     13  alpha,,0,, = (b,,0,,^2^+b,,1,,^2^) / b,,0,,(a,,0,,b,,0,, + a,,1,,b,,1,,) + b,,1,,(a,,1,,b,,0,, + a,,2,,b,,1,,)
    1414
    15 Step 3: r,,1,, = r,,0,, - alpha,,0,, * Ap,,0,,
    16   r[0] = (-b,,1,,*(-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^)
     15Step 3: r,,1,, = r,,0,, - alpha,,0,, Ap,,0,,
     16  r[0] = (-b,,1,,(-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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)
    1717
    18   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^)
     18  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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)
    1919
    20 Step 4: x,,1,, = x,,0,, + alpha*p,,0,,
    21   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^)
     20Step 4: x,,1,, = x,,0,, + alphap,,0,,
     21  x[0] = (b,,0,,(b,,0,,^2^ + b,,1,,^2^)) / (a,,0,,b,,0,,^2^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)
    2222
    23   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^)
     23  x[1] = (b,,1,,(b,,0,,^2^ + b,,1,,^2^)) / (a,,0,,b,,0,,^2^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)
    2424
    2525Step 5: beta = rsnew / rsold = <r,,1,,, r,,1,,> / <r,,0,,, r,,0,,>
    26   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^
     26  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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)^2^
    2727
    28   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^
     28  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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)^2^
    2929
    30 Step 6: p,,1,, = r,,1,, +beta * p,,0,,
    31   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^
     30Step 6: p,,1,, = r,,1,, +beta p,,0,,
     31  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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)^2^
    3232
    33   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^
     33  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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)^2^
    3434
    3535Step 7: alpha,,1,, = <r,,1,,, r,,1,,> / <p,,1,,, Ap,,1,,>
    36   <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^
     36  <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^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^)^3^
    3737
    38   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^))
     38  alpha,,1,, = (a,,0,,b,,0,,^2^ + 2a,,1,,b,,0,,b,,1,, + a,,2,,b,,1,,^2^) / ((-a,,1,,^2^ + a,,0,,a,,2,,) (b,,0,,^2^ + b,,1,,^2^))
    3939
    40 Step 8: r,,2,, = r,,1,, - alpha,,1,, * Ap,,1,,
     40Step 8: r,,2,, = r,,1,, - alpha,,1,, Ap,,1,,
    4141  r[0] = 0
    4242
    4343  r[1] = 0
    4444
    45 Step 9: x,,2,, = x,,1,, + alpha,,1,,*p,,1,,
    46   x[0] = (a,,2,,*b,,0,, - a,,1,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^)
     45Step 9: x,,2,, = x,,1,, + alpha,,1,,p,,1,,
     46  x[0] = (a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^)
    4747
    48   x[1] = (-a,,1,,*b,,0,, + a,,0,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^)
     48  x[1] = (-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^)
    4949
    5050assertion: 
    51   bncg[0] = A[0][0]*x[0] + A[0][1]*x[1] = a,,0,,*(a,,2,,*b,,0,, - a,,1,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^) + a,,1,,*(-a,,1,,*b,,0,, + a,,0,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^) = b,,0,,*(a,,0,,*a,,2,, - a,,1,,^2^) / (a,,0,,*a,,2,, - a,,1,,^2^) = b,,0,,
     51  bncg[0] = A[0][0]x[0] + A[0][1]x[1] = a,,0,,(a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) + a,,1,,(-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,0,,(a,,0,,a,,2,, - a,,1,,^2^) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,0,,
    5252
    53   bncg[1] = A[1][0]*x[0] + A[1][1]*x[1] = a,,1,,*(a,,2,,*b,,0,, - a,,1,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^) + a,,2,,*(-a,,1,,*b,,0,, + a,,0,,*b,,1,,) / (a,,0,,*a,,2,, - a,,1,,^2^) = b,,1,,*(a,,0,,*a,,2,, - a,,1,,^2^) / (a,,0,,*a,,2,, - a,,1,,^2^) = b,,1,,
     53  bncg[1] = A[1][0]x[0] + A[1][1]x[1] = a,,1,,(a,,2,,b,,0,, - a,,1,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) + a,,2,,(-a,,1,,b,,0,, + a,,0,,b,,1,,) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,1,,(a,,0,,a,,2,, - a,,1,,^2^) / (a,,0,,a,,2,, - a,,1,,^2^) = b,,1,,
    5454
    5555  b[0] = b,,0,,