Changes between Version 29 and Version 30 of PolynomialExpansion


Ignore:
Timestamp:
01/26/16 16:09:45 (10 years ago)
Author:
sili
Comment:

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  • PolynomialExpansion

    v29 v30  
    11
    22A = {{a,,0,,, a,,1,,}, {a,,1,,, a,,2,,}},  b = {b,,0,,, b,,1,,}
    3    
    43
    5 Step 1: r = b - Ax
     4x[0] = 0, x[1] = 0
     5
     6k = 0
     7
     8Step 1: r,,0,, = b - Ax,,0,,
    69  r[0] = b,,0,,
    710
    811  r[1] = b,,1,,
    912
    10 Step 2: alpha = (r[i]*r[i]) / (p[i]*A[i][j]*p[j])
    11   p[i]*(A[i][j]*p[j]) = a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^
     13  p,,0,, = r,,0,,
     14
     15Step 2: alpha = <r, r> / <p, Ap>
     16  <p, Ap> = a,,0,,*b,,0,,^2^ + 2*a,,1,,*b,,0,,*b,,1,, + a,,2,,*b,,1,,^2^
    1217
    1318  alpha = (b,,0,,^2^+b,,1,,^2^) / ((b,,1,,^2^)*a,,2,,+2*(b,,1,,*b,,0,,*a,,1,,)+(b,,0,,^2^)*a,,0,,)
    1419
    15 Step 3: r[i] = r - alpha * A[i][j] * p[j]
     20Step 3: r[i] = r - alpha * Ap
    1621  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^)
    1722
    1823  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^)
    1924
    20 Step 4: x[i] = x + alpha*p[i]
     25Step 4: x[i] = x + alpha*p
    2126  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^)
    2227
    2328  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^)
    2429
    25 Step 5: beta = rsnew / rsold = (rk[i]*rk[i]) / (r[i]*r[i])
     30Step 5: beta = rsnew / rsold = <r,,k+1,,, r,,k+1,,> / <r,,k,,, r,,k,,>
    2631  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^
    2732
    2833  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^
    2934
    30 Step 6: p[i] = rk[i] +beta * p
     35Step 6: p[i] = r[i] +beta * p
    3136  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^
    3237