octave:2> prod([1,2,3,4]) ans = 24 octave:3> prod([1,2,3,4]') ans = 24 octave:4> v=[1,2,3,4] v = 1 2 3 4 octave:5> v([1:2,4]) ans = 1 2 4 octave:6> v=[10,20,30,40] v = 10 20 30 40 octave:7> v([1,3:4]) ans = 10 30 40 octave:8> 50-v ans = 40 30 20 10 octave:9> 50-v([1:3]) ans = 40 30 20 octave:10> nodi=1:10 nodi = 1 2 3 4 5 6 7 8 9 10 octave:11> lagrangesemplice(1,1,nodi) ans = 1 octave:12> lagrangesemplice(1,2,nodi) ans = -0 octave:13> lagrangesemplice(1,3,nodi) ans = 0 octave:14> lagrangesemplice(1,4,nodi) ans = -0 octave:15> lagrangesemplice(1,5,nodi) ans = 0 octave:16> lagrangesemplice(1,6,nodi) ans = -0 octave:17> lagrangesemplice(1,1.5,nodi) ans = 0.18547 octave:18> lagrangesemplice(1,sqrt(2),nodi) ans = 0.26079 octave:19> lagrangesemplice(5,5,nodi) ans = 1 octave:20> lagrangesemplice(5,1,nodi) ans = -0 octave:21> lagrangesemplice(5,2,nodi) ans = 0 octave:22> lagrangesemplice(5,3,nodi) ans = -0 octave:23> lagrangesemplice(5,3.6,nodi) ans = -0.43016 octave:24> lagrangesemplice(5,[,nodi) parse error: syntax error >>> lagrangesemplice(5,[,nodi) ^ octave:24> lagrangesemplice(5,nodi,nodi) error: operator -: nonconformant arguments (op1 is 1x10, op2 is 1x9) error: evaluating binary operator `-' near line 3, column 11 error: evaluating argument list element number 1 error: evaluating binary operator `/' near line 3, column 32 error: evaluating assignment expression near line 3, column 3 error: called from `lagrangesemplice' in file `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrangesemplice.m' octave:24> xbar=[1,2,3,4]' xbar = 1 2 3 4 octave:25> repmat(xbar,1,5) ans = 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 octave:26> n=4 n = 4 octave:27> x=[1,2,3,4] x = 1 2 3 4 octave:28> m=7 m = 7 octave:29> xbar=[1:0.5:4]' xbar = 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 octave:30> repmat(xbar,1,n-1) ans = 1.0000 1.0000 1.0000 1.5000 1.5000 1.5000 2.0000 2.0000 2.0000 2.5000 2.5000 2.5000 3.0000 3.0000 3.0000 3.5000 3.5000 3.5000 4.0000 4.0000 4.0000 octave:31> i=2 i = 2 octave:32> repmat(x([1:i-1:i+1:n]),m,1) error: invalid colon expression octave:32> repmat(x([1:i-1,i+1:n]),m,1) ans = 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 1 3 4 octave:33> repmat(xbar,1,n-1)-repmat(x([1:i-1,i+1:n]),m,1) ans = 0.00000 -2.00000 -3.00000 0.50000 -1.50000 -2.50000 1.00000 -1.00000 -2.00000 1.50000 -0.50000 -1.50000 2.00000 0.00000 -1.00000 2.50000 0.50000 -0.50000 3.00000 1.00000 0.00000 octave:34> prod(ans) ans = 0 0 0 octave:35> prod(repmat(xbar,1,n-1)-repmat(x([1:i-1,i+1:n]),m,1),2) ans = 0.00000 1.87500 2.00000 1.12500 -0.00000 -0.62500 0.00000 octave:36> prod(1-x([1:i-1,i+1:n])) ans = 0 octave:37> prod(1.5-x([1:i-1,i+1:n])) ans = 1.8750 octave:38> prod(2-x([1:i-1,i+1:n])) ans = 2 octave:39> lagrange(1,xbar,x) warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrange.m' is in the future ans = 1.00000 0.31250 -0.00000 -0.06250 0.00000 0.06250 -0.00000 octave:40> xbar=linspace(1,4,100)'; octave:41> plot(xbar,lagrange(1,xbar,x)) warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrange.m' is in the future octave:42> plot(xbar,lagrange(1,xbar,x),xbar,zeros(size(xbar))) warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrange.m' is in the future octave:43> plot(xbar,lagrange(2,xbar,x),xbar,zeros(size(xbar))) warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrange.m' is in the future octave:44> plot(xbar,lagrange(2,xbar,x),x,zeros(size(x)),'*') warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrange.m' is in the future octave:45> plot(xbar,lagrange(4,xbar,x),x,zeros(size(x)),'*') warning: time stamp for `/home/accounts/altri/caliari/aa0809/calcolo_numerico/interpolazione/lagrange.m' is in the future octave:46> x x = 1 2 3 4 octave:47> repmat(x',1,4) ans = 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 octave:48> repmat([3:-1:0],4,1) ans = 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 0 octave:49> vander(x) ans = 1 1 1 1 8 4 2 1 27 9 3 1 64 16 4 1 octave:50> x x = 1 2 3 4 octave:51> y=sin(x) y = 0.84147 0.90930 0.14112 -0.75680 octave:52> polyfit(x,y,3) ans = 0.11771 -1.12426 2.61664 -0.76862 octave:53> x=cos(linspace(0,pi,30)) x = Columns 1 through 6: 1.000000 0.994138 0.976621 0.947653 0.907575 0.856857 Columns 7 through 12: 0.796093 0.725995 0.647386 0.561187 0.468408 0.370138 Columns 13 through 18: 0.267528 0.161782 0.054139 -0.054139 -0.161782 -0.267528 Columns 19 through 24: -0.370138 -0.468408 -0.561187 -0.647386 -0.725995 -0.796093 Columns 25 through 30: -0.856857 -0.907575 -0.947653 -0.976621 -0.994138 -1.000000 octave:54> x=x*5 x = Columns 1 through 7: 5.00000 4.97069 4.88310 4.73827 4.53788 4.28429 3.98047 Columns 8 through 14: 3.62998 3.23693 2.80594 2.34204 1.85069 1.33764 0.80891 Columns 15 through 21: 0.27069 -0.27069 -0.80891 -1.33764 -1.85069 -2.34204 -2.80594 Columns 22 through 28: -3.23693 -3.62998 -3.98047 -4.28429 -4.53788 -4.73827 -4.88310 Columns 29 and 30: -4.97069 -5.00000 octave:55> V=vander(x); octave:56> cond(V) ans = 8.9328e+21 octave:57> inv(V) warning: inverse: matrix singular to machine precision, rcond = 3.08384e-23 ans = Columns 1 through 5: 2.4847e-14 -4.9695e-14 4.9695e-14 -4.9695e-14 4.9695e-14 1.2424e-13 -2.4702e-13 2.4267e-13 -2.3547e-13 2.2551e-13 -4.1930e-12 8.4005e-12 -8.4434e-12 8.5127e-12 -8.6051e-12 -2.0965e-11 4.1756e-11 -4.1230e-11 4.0335e-11 -3.9049e-11 3.1545e-10 -6.3298e-10 6.3921e-10 -6.4942e-10 6.6334e-10 1.5772e-09 -3.1464e-09 3.1213e-09 -3.0771e-09 3.0102e-09 -1.3952e-08 2.8038e-08 -2.8435e-08 2.9097e-08 -3.0017e-08 -6.9762e-08 1.3937e-07 -1.3885e-07 1.3787e-07 -1.3622e-07 4.0288e-07 -8.1063e-07 8.2534e-07 -8.5012e-07 8.8525e-07 2.0144e-06 -4.0294e-06 4.0302e-06 -4.0281e-06 4.0171e-06 -7.9736e-06 1.6062e-05 -1.6411e-05 1.7005e-05 -1.7862e-05 -3.9868e-05 7.9840e-05 -8.0137e-05 8.0574e-05 -8.1054e-05 1.1050e-04 -2.2283e-04 2.2837e-04 -2.3791e-04 2.5187e-04 5.5252e-04 -1.1076e-03 1.1152e-03 -1.1273e-03 1.1430e-03 -1.0763e-03 2.1723e-03 -2.2324e-03 2.3366e-03 -2.4912e-03 -5.3817e-03 1.0798e-02 -1.0901e-02 1.1071e-02 -1.1305e-02 7.2877e-03 -1.4719e-02 1.5161e-02 -1.5933e-02 1.7092e-02 3.6438e-02 -7.3165e-02 7.4035e-02 -7.5497e-02 7.7563e-02 -3.3402e-02 6.7506e-02 -6.9667e-02 7.3463e-02 -7.9216e-02 -1.6701e-01 3.3555e-01 -3.4019e-01 3.4809e-01 -3.5947e-01 9.8887e-02 -1.9995e-01 2.0667e-01 -2.1853e-01 2.3663e-01 4.9444e-01 -9.9390e-01 1.0092e+00 -1.0355e+00 1.0738e+00 -1.7480e-01 3.5358e-01 -3.6590e-01 3.8769e-01 -4.2115e-01 -8.7400e-01 1.7576e+00 -1.7867e+00 1.8370e+00 -1.9111e+00 1.6066e-01 -3.2507e-01 3.3666e-01 -3.5722e-01 3.8890e-01 8.0331e-01 -1.6158e+00 1.6439e+00 -1.6926e+00 1.7648e+00 -5.7931e-02 1.1723e-01 -1.2146e-01 1.2898e-01 -1.4059e-01 -2.8966e-01 5.8271e-01 -5.9311e-01 6.1115e-01 -6.3798e-01 3.4483e-03 -6.9781e-03 7.2307e-03 -7.6795e-03 8.3727e-03 1.7241e-02 -3.4686e-02 3.5308e-02 -3.6388e-02 3.7994e-02 Columns 6 through 10: -4.9695e-14 4.9695e-14 -4.9695e-14 4.9695e-14 -4.9695e-14 -2.1291e-13 1.9781e-13 -1.8039e-13 1.6086e-13 -1.3944e-13 8.7162e-12 -8.8410e-12 8.9736e-12 -9.1077e-12 9.2371e-12 3.7343e-11 -3.5191e-11 3.2574e-11 -2.9481e-11 2.5919e-11 -6.8056e-10 7.0046e-10 -7.2230e-10 7.4511e-10 -7.6782e-10 -2.9157e-09 2.7882e-09 -2.6219e-09 2.4119e-09 -2.1544e-09 3.1185e-08 -3.2579e-08 3.4160e-08 -3.5870e-08 3.7632e-08 1.3361e-07 -1.2968e-07 1.2400e-07 -1.1611e-07 1.0559e-07 -9.3096e-07 9.8719e-07 -1.0533e-06 1.1275e-06 -1.2071e-06 -3.9885e-06 3.9295e-06 -3.8233e-06 3.6498e-06 -3.3870e-06 1.9003e-05 -2.0450e-05 2.2212e-05 -2.4277e-05 2.6587e-05 8.1415e-05 -8.1400e-05 8.0631e-05 -7.8583e-05 7.4602e-05 -2.7088e-04 2.9568e-04 -3.2700e-04 3.6532e-04 -4.1036e-04 -1.1605e-03 1.1769e-03 -1.1870e-03 1.1825e-03 -1.1514e-03 2.7058e-03 -2.9931e-03 3.3691e-03 -3.8501e-03 4.4470e-03 1.1592e-02 -1.1914e-02 1.2230e-02 -1.2463e-02 1.2478e-02 -1.8727e-02 2.0969e-02 -2.3999e-02 2.8051e-02 -3.3380e-02 -8.0233e-02 8.3466e-02 -8.7115e-02 9.0801e-02 -9.3661e-02 8.7444e-02 -9.8954e-02 1.1496e-01 -1.3727e-01 1.6838e-01 3.7464e-01 -3.9388e-01 4.1731e-01 -4.4434e-01 4.7246e-01 -2.6282e-01 3.0003e-01 -3.5304e-01 4.2956e-01 -5.4216e-01 -1.1260e+00 1.1943e+00 -1.2815e+00 1.3905e+00 -1.5213e+00 4.6995e-01 -5.4017e-01 6.4201e-01 -7.9310e-01 1.0253e+00 2.0134e+00 -2.1501e+00 2.3305e+00 -2.5672e+00 2.8770e+00 -4.3537e-01 5.0280e-01 -6.0179e-01 7.5144e-01 -9.8853e-01 -1.8653e+00 2.0014e+00 -2.1845e+00 2.4324e+00 -2.7738e+00 1.5767e-01 -1.8256e-01 2.1935e-01 -2.7554e-01 3.6599e-01 6.7550e-01 -7.2669e-01 7.9625e-01 -8.9189e-01 1.0269e+00 -9.3932e-03 1.0882e-02 -1.3085e-02 1.6455e-02 -2.1899e-02 -4.0243e-02 4.3315e-02 -4.7497e-02 5.3265e-02 -6.1446e-02 Columns 11 through 15: 4.9695e-14 -4.9695e-14 4.9695e-14 -4.9695e-14 4.9695e-14 1.1639e-13 -9.1970e-14 6.6474e-14 -4.0199e-14 1.3452e-14 -9.3558e-12 9.4582e-12 -9.5395e-12 9.5959e-12 -9.6247e-12 -2.1912e-11 1.7504e-11 -1.2760e-11 7.7622e-12 -2.6054e-12 7.8922e-10 -8.0815e-10 8.2347e-10 -8.3426e-10 8.3984e-10 1.8484e-09 -1.4956e-09 1.1015e-09 -6.7484e-10 2.2734e-10 -3.9348e-08 4.0909e-08 -4.2204e-08 4.3131e-08 -4.3616e-08 -9.2155e-08 7.5710e-08 -5.6453e-08 3.4889e-08 -1.1807e-08 1.2875e-06 -1.3633e-06 1.4279e-06 -1.4752e-06 1.5002e-06 3.0155e-06 -2.5230e-06 1.9100e-06 -1.1933e-06 4.0609e-07 -2.9029e-05 3.1422e-05 -3.3536e-05 3.5126e-05 -3.5981e-05 -6.7986e-05 5.8152e-05 -4.4859e-05 2.8414e-05 -9.7399e-06 4.6046e-04 -5.1207e-04 5.5968e-04 -5.9670e-04 6.1705e-04 1.0784e-03 -9.4767e-04 7.4865e-04 -4.8268e-04 1.6703e-04 -5.1521e-03 5.9240e-03 -6.6764e-03 7.2874e-03 -7.6326e-03 -1.2067e-02 1.0963e-02 -8.9307e-03 5.8949e-03 -2.0661e-03 4.0132e-02 -4.8102e-02 5.6446e-02 -6.3624e-02 6.7833e-02 9.3990e-02 -8.9022e-02 7.5505e-02 -5.1466e-02 1.8362e-02 -2.1106e-01 2.6644e-01 -3.3019e-01 3.8956e-01 -4.2622e-01 -4.9431e-01 4.9309e-01 -4.4168e-01 3.1512e-01 -1.1537e-01 7.1017e-01 -9.5531e-01 1.2771e+00 -1.6130e+00 1.8366e+00 1.6633e+00 -1.7680e+00 1.7083e+00 -1.3047e+00 4.9717e-01 -1.3985e+00 2.0220e+00 -3.0089e+00 4.2385e+00 -5.1594e+00 -3.2754e+00 3.7420e+00 -4.0249e+00 3.4286e+00 -1.3966e+00 1.3902e+00 -2.1360e+00 3.6775e+00 -6.2879e+00 8.6833e+00 3.2559e+00 -3.9531e+00 4.9192e+00 -5.0864e+00 2.3505e+00 -5.2360e-01 8.3301e-01 -1.5688e+00 4.0346e+00 -7.5127e+00 -1.2263e+00 1.5416e+00 -2.0985e+00 3.2636e+00 -2.0336e+00 3.1433e-02 -5.0339e-02 9.6359e-02 -2.6349e-01 2.3530e+00 7.3617e-02 -9.3162e-02 1.2889e-01 -2.1314e-01 6.3693e-01 Columns 16 through 20: -4.9695e-14 4.9695e-14 -4.9695e-14 4.9695e-14 -4.9695e-14 1.3452e-14 -4.0199e-14 6.6474e-14 -9.1970e-14 1.1639e-13 9.6247e-12 -9.5959e-12 9.5395e-12 -9.4582e-12 9.3558e-12 -2.6054e-12 7.7622e-12 -1.2760e-11 1.7504e-11 -2.1912e-11 -8.3984e-10 8.3426e-10 -8.2347e-10 8.0815e-10 -7.8922e-10 2.2734e-10 -6.7484e-10 1.1015e-09 -1.4956e-09 1.8484e-09 4.3616e-08 -4.3131e-08 4.2204e-08 -4.0909e-08 3.9348e-08 -1.1807e-08 3.4889e-08 -5.6453e-08 7.5710e-08 -9.2155e-08 -1.5002e-06 1.4752e-06 -1.4279e-06 1.3633e-06 -1.2875e-06 4.0609e-07 -1.1933e-06 1.9100e-06 -2.5230e-06 3.0155e-06 3.5981e-05 -3.5126e-05 3.3536e-05 -3.1422e-05 2.9029e-05 -9.7399e-06 2.8414e-05 -4.4859e-05 5.8152e-05 -6.7986e-05 -6.1705e-04 5.9670e-04 -5.5968e-04 5.1207e-04 -4.6046e-04 1.6703e-04 -4.8268e-04 7.4865e-04 -9.4767e-04 1.0784e-03 7.6326e-03 -7.2874e-03 6.6764e-03 -5.9240e-03 5.1521e-03 -2.0661e-03 5.8949e-03 -8.9307e-03 1.0963e-02 -1.2067e-02 -6.7833e-02 6.3624e-02 -5.6446e-02 4.8102e-02 -4.0132e-02 1.8362e-02 -5.1466e-02 7.5505e-02 -8.9022e-02 9.3990e-02 4.2622e-01 -3.8956e-01 3.3019e-01 -2.6644e-01 2.1106e-01 -1.1537e-01 3.1512e-01 -4.4168e-01 4.9309e-01 -4.9431e-01 -1.8366e+00 1.6130e+00 -1.2771e+00 9.5531e-01 -7.1017e-01 4.9717e-01 -1.3047e+00 1.7083e+00 -1.7680e+00 1.6633e+00 5.1594e+00 -4.2385e+00 3.0089e+00 -2.0220e+00 1.3985e+00 -1.3966e+00 3.4286e+00 -4.0249e+00 3.7420e+00 -3.2754e+00 -8.6833e+00 6.2879e+00 -3.6775e+00 2.1360e+00 -1.3902e+00 2.3505e+00 -5.0864e+00 4.9192e+00 -3.9531e+00 3.2559e+00 7.5127e+00 -4.0346e+00 1.5688e+00 -8.3301e-01 5.2360e-01 -2.0336e+00 3.2636e+00 -2.0985e+00 1.5416e+00 -1.2263e+00 -2.3530e+00 2.6349e-01 -9.6359e-02 5.0339e-02 -3.1433e-02 6.3693e-01 -2.1314e-01 1.2889e-01 -9.3162e-02 7.3617e-02 Columns 21 through 25: 4.9695e-14 -4.9695e-14 4.9695e-14 -4.9695e-14 4.9695e-14 -1.3944e-13 1.6086e-13 -1.8039e-13 1.9781e-13 -2.1291e-13 -9.2371e-12 9.1077e-12 -8.9736e-12 8.8410e-12 -8.7162e-12 2.5919e-11 -2.9481e-11 3.2574e-11 -3.5191e-11 3.7343e-11 7.6782e-10 -7.4511e-10 7.2230e-10 -7.0046e-10 6.8056e-10 -2.1544e-09 2.4119e-09 -2.6219e-09 2.7882e-09 -2.9157e-09 -3.7632e-08 3.5870e-08 -3.4160e-08 3.2579e-08 -3.1185e-08 1.0559e-07 -1.1611e-07 1.2400e-07 -1.2968e-07 1.3361e-07 1.2071e-06 -1.1275e-06 1.0533e-06 -9.8719e-07 9.3096e-07 -3.3870e-06 3.6498e-06 -3.8233e-06 3.9295e-06 -3.9885e-06 -2.6587e-05 2.4277e-05 -2.2212e-05 2.0450e-05 -1.9003e-05 7.4602e-05 -7.8583e-05 8.0631e-05 -8.1400e-05 8.1415e-05 4.1036e-04 -3.6532e-04 3.2700e-04 -2.9568e-04 2.7088e-04 -1.1514e-03 1.1825e-03 -1.1870e-03 1.1769e-03 -1.1605e-03 -4.4470e-03 3.8501e-03 -3.3691e-03 2.9931e-03 -2.7058e-03 1.2478e-02 -1.2463e-02 1.2230e-02 -1.1914e-02 1.1592e-02 3.3380e-02 -2.8051e-02 2.3999e-02 -2.0969e-02 1.8727e-02 -9.3661e-02 9.0801e-02 -8.7115e-02 8.3466e-02 -8.0233e-02 -1.6838e-01 1.3727e-01 -1.1496e-01 9.8954e-02 -8.7444e-02 4.7246e-01 -4.4434e-01 4.1731e-01 -3.9388e-01 3.7464e-01 5.4216e-01 -4.2956e-01 3.5304e-01 -3.0003e-01 2.6282e-01 -1.5213e+00 1.3905e+00 -1.2815e+00 1.1943e+00 -1.1260e+00 -1.0253e+00 7.9310e-01 -6.4201e-01 5.4017e-01 -4.6995e-01 2.8770e+00 -2.5672e+00 2.3305e+00 -2.1501e+00 2.0134e+00 9.8853e-01 -7.5144e-01 6.0179e-01 -5.0280e-01 4.3537e-01 -2.7738e+00 2.4324e+00 -2.1845e+00 2.0014e+00 -1.8653e+00 -3.6599e-01 2.7554e-01 -2.1935e-01 1.8256e-01 -1.5767e-01 1.0269e+00 -8.9189e-01 7.9625e-01 -7.2669e-01 6.7550e-01 2.1899e-02 -1.6455e-02 1.3085e-02 -1.0882e-02 9.3932e-03 -6.1446e-02 5.3265e-02 -4.7497e-02 4.3315e-02 -4.0243e-02 Columns 26 through 30: -4.9695e-14 4.9695e-14 -4.9695e-14 4.9695e-14 -2.4847e-14 2.2551e-13 -2.3547e-13 2.4267e-13 -2.4702e-13 1.2424e-13 8.6051e-12 -8.5127e-12 8.4434e-12 -8.4005e-12 4.1930e-12 -3.9049e-11 4.0335e-11 -4.1230e-11 4.1756e-11 -2.0965e-11 -6.6334e-10 6.4942e-10 -6.3921e-10 6.3298e-10 -3.1545e-10 3.0102e-09 -3.0771e-09 3.1213e-09 -3.1464e-09 1.5772e-09 3.0017e-08 -2.9097e-08 2.8435e-08 -2.8038e-08 1.3952e-08 -1.3622e-07 1.3787e-07 -1.3885e-07 1.3937e-07 -6.9762e-08 -8.8525e-07 8.5012e-07 -8.2534e-07 8.1063e-07 -4.0288e-07 4.0171e-06 -4.0281e-06 4.0302e-06 -4.0294e-06 2.0144e-06 1.7862e-05 -1.7005e-05 1.6411e-05 -1.6062e-05 7.9736e-06 -8.1054e-05 8.0574e-05 -8.0137e-05 7.9840e-05 -3.9868e-05 -2.5187e-04 2.3791e-04 -2.2837e-04 2.2283e-04 -1.1050e-04 1.1430e-03 -1.1273e-03 1.1152e-03 -1.1076e-03 5.5252e-04 2.4912e-03 -2.3366e-03 2.2324e-03 -2.1723e-03 1.0763e-03 -1.1305e-02 1.1071e-02 -1.0901e-02 1.0798e-02 -5.3817e-03 -1.7092e-02 1.5933e-02 -1.5161e-02 1.4719e-02 -7.2877e-03 7.7563e-02 -7.5497e-02 7.4035e-02 -7.3165e-02 3.6438e-02 7.9216e-02 -7.3463e-02 6.9667e-02 -6.7506e-02 3.3402e-02 -3.5947e-01 3.4809e-01 -3.4019e-01 3.3555e-01 -1.6701e-01 -2.3663e-01 2.1853e-01 -2.0667e-01 1.9995e-01 -9.8887e-02 1.0738e+00 -1.0355e+00 1.0092e+00 -9.9390e-01 4.9444e-01 4.2115e-01 -3.8769e-01 3.6590e-01 -3.5358e-01 1.7480e-01 -1.9111e+00 1.8370e+00 -1.7867e+00 1.7576e+00 -8.7400e-01 -3.8890e-01 3.5722e-01 -3.3666e-01 3.2507e-01 -1.6066e-01 1.7648e+00 -1.6926e+00 1.6439e+00 -1.6158e+00 8.0331e-01 1.4059e-01 -1.2898e-01 1.2146e-01 -1.1723e-01 5.7931e-02 -6.3798e-01 6.1115e-01 -5.9311e-01 5.8271e-01 -2.8966e-01 -8.3727e-03 7.6795e-03 -7.2307e-03 6.9781e-03 -3.4483e-03 3.7994e-02 -3.6388e-02 3.5308e-02 -3.4686e-02 1.7241e-02 octave:58> inv(V); warning: inverse: matrix singular to machine precision, rcond = 3.08384e-23 octave:59> xhat=(x-mean(x))/std(x); octave:60> Vhat=vander(xhat); octave:61> cond(Vhat) ans = 2.9384e+11 octave:62> x=linspace(-5,5,5) x = -5.00000 -2.50000 0.00000 2.50000 5.00000 octave:63> y=1./(1+x.^2); octave:64> Vx=vander(x); octave:65> a=Vx\y'; octave:66> xbar=linspace(-5,5,100); octave:67> ybar=polyval(a,xbar); octave:68> plot(xbar,ybar) octave:69> plot(xbar,ybar,xbar,1./(1+xbar.^2)) octave:70> xhat=(x-mean(x))/std(x); octave:71> Vxhat=vander(xhat); octave:72> ahat=Vxhat\y'; octave:73> ybarhat=polyval(ahat,(xbar-mean(x))/std(x)); octave:74> plot(xbar,ybar,'*',xbar,ybarhat) octave:75> a a = 5.3050e-03 -9.2519e-20 -1.7109e-01 2.3130e-18 1.0000e+00 octave:76> ahat ahat = 1.2952e+00 -5.7142e-18 -2.6732e+00 9.1428e-18 1.0000e+00 octave:77> cond(Vx) ans = 904.30 octave:78> cond(Vxhat) ans = 20.932 octave:79> diary off