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>> t=[0.1:0.1:1]';
>> f = [100;34;17;12;9;6;5;4;4;2];
>> A=[1./t 1./t.^2 exp(-(t-1)) exp(-2*(t-1))]

A =

   1.0e+02 *

   0.100000000000000   1.000000000000000   0.024596031111569   0.060496474644129
   0.050000000000000   0.250000000000000   0.022255409284925   0.049530324243951
   0.033333333333333   0.111111111111111   0.020137527074705   0.040551999668447
   0.025000000000000   0.062500000000000   0.018221188003905   0.033201169227365
   0.020000000000000   0.040000000000000   0.016487212707001   0.027182818284590
   0.016666666666667   0.027777777777778   0.014918246976413   0.022255409284925
   0.014285714285714   0.020408163265306   0.013498588075760   0.018221188003905
   0.012500000000000   0.015625000000000   0.012214027581602   0.014918246976413
   0.011111111111111   0.012345679012346   0.011051709180756   0.012214027581602
   0.010000000000000   0.010000000000000   0.010000000000000   0.010000000000000

>> [L,R,P] = lu(A'*A)

L =

   1.000000000000000                   0                   0                   0
   0.102752982142445   1.000000000000000                   0                   0
   0.048815773086868   0.600370490387472   1.000000000000000                   0
   0.129413472851336   0.695336126107029   0.087558532993088   1.000000000000000


R =

   1.0e+04 *

   0.119753198567419   1.082036583493756   0.035312861373317   0.082021174120268
                   0  -0.029161311620938   0.001826709405378   0.002469895646790
                   0                   0   0.000065189529803  -0.000031568265373
                   0                   0                   0  -0.000024290316272


P =

     0     1     0     0
     0     0     0     1
     0     0     1     0
     1     0     0     0

>> c = P*(A'*f)

c =

   1.0e+04 *

   1.118994790879315
   0.094192893723217
   0.041957295268110
   0.130325396825397

>> R\(L\c)

ans =

   4.059115646964496
   0.614035171352509
  -2.531459328992657
   0.705759979941432

>>