>> lininva --------------------------------------------------------- Part A(b): Calculate data vector. --------------------------------------------------------- d = 0.17227012335877 0.06370498927031 0.02445236255442 0.00970951743466 0.00397209406548 0.00166693485108 0.00071470445837 0.00031194465707 0.00013818042394 --------------------------------------------------------- Part A(c): Fit data exactly with minimum-norm function. --------------------------------------------------------- Minimum-norm solution assuming data exact is x=G'*lambda, where lambda is given below: -2.89127e-01 2.52969e+01 -4.88487e+02 3.51580e+03 -1.14471e+04 1.90896e+04 -1.67350e+04 7.14543e+03 -1.10496e+03 This x has N(x) = 1.109e-01, E(x) = 8.255e-27. Figure number 1 saved as minnormx.eps. --------------------------------------------------------- Part A(d): Tradeoff between E and N using various mu. --------------------------------------------------------- k mu cond(LHS) E N |(E,N)| 1 1.000e-05 4.053e+05 1.755e+02 4.325e-04 1.755e+02 2 1.887e-05 3.697e+05 1.517e+02 7.607e-04 1.517e+02 3 3.562e-05 3.456e+05 1.312e+02 1.300e-03 1.312e+02 4 6.723e-05 3.343e+05 1.089e+02 2.420e-03 1.089e+02 5 1.269e-04 3.369e+05 8.227e+01 4.942e-03 8.227e+01 6 2.395e-04 3.587e+05 5.403e+01 9.936e-03 5.403e+01 7 4.520e-04 4.137e+05 3.037e+01 1.772e-02 3.037e+01 8 8.532e-04 5.288e+05 1.515e+01 2.704e-02 1.515e+01 9 1.610e-03 7.487e+05 7.299e+00 3.604e-02 7.299e+00 10 3.039e-03 1.148e+06 3.702e+00 4.380e-02 3.702e+00 11 5.736e-03 1.849e+06 1.996e+00 5.079e-02 1.997e+00 12 1.083e-02 3.058e+06 1.055e+00 5.813e-02 1.056e+00 13 2.043e-02 5.126e+06 4.991e-01 6.628e-02 5.035e-01 14 3.857e-02 8.664e+06 2.052e-01 7.435e-02 2.183e-01 15 7.279e-02 1.468e+07 7.554e-02 8.101e-02 1.108e-01 16 1.374e-01 2.480e+07 2.673e-02 8.571e-02 8.978e-02 17 1.873e-01 3.196e+07 1.637e-02 8.736e-02 8.888e-02 18 2.593e-01 4.168e+07 1.012e-02 8.872e-02 8.929e-02 19 4.894e-01 7.011e+07 4.637e-03 9.059e-02 9.071e-02 20 9.237e-01 1.183e+08 2.664e-03 9.188e-02 9.192e-02 21 1.743e+00 1.988e+08 1.699e-03 9.310e-02 9.311e-02 22 3.290e+00 3.302e+08 1.028e-03 9.471e-02 9.471e-02 23 6.210e+00 5.422e+08 5.389e-04 9.691e-02 9.691e-02 24 1.172e+01 8.900e+08 2.428e-04 9.939e-02 9.939e-02 25 2.212e+01 1.474e+09 1.001e-04 1.016e-01 1.016e-01 26 4.175e+01 2.450e+09 4.194e-05 1.033e-01 1.033e-01 27 7.880e+01 4.024e+09 1.926e-05 1.046e-01 1.046e-01 28 1.487e+02 6.435e+09 9.305e-06 1.057e-01 1.057e-01 29 2.807e+02 1.004e+10 4.257e-06 1.067e-01 1.067e-01 30 5.298e+02 1.559e+10 1.747e-06 1.076e-01 1.076e-01 31 1.000e+03 2.468e+10 6.592e-07 1.084e-01 1.084e-01 Figure number 2 saved as tradeoff.eps. Figure number 3 saved as regcond.eps. --------------------------------------------------------- Part A(e): Choose mu to hit misfit targets. --------------------------------------------------------- For target misfit of 8 use mu = 2.8162e-03. Actual misfit then equals 7.9997e+00, with lambda shown below: 1.3959e-01 8.4357e-01 1.7166e+00 1.8346e+00 -1.7125e+00 -1.2299e+01 -1.8040e+01 4.0941e+01 -1.2804e+01 For target misfit of 10 use mu = 2.2738e-03. Actual misfit then equals 9.9998e+00, with lambda shown below: 1.4638e-01 7.5590e-01 1.5372e+00 1.7442e+00 -1.0717e+00 -1.0031e+01 -1.6354e+01 2.8794e+01 -4.8593e+00 Figure number 4 saved as misfits.eps. --------------------------------------------------------- Part A(f): Choose mu to hit corner of tradeoff curve. --------------------------------------------------------- it= 1: [mulo,muhi]=[ 8.000e-04, 3.000e-01], [Flo,Fhi]=[-16.3049, 0.0185]. it= 2: [mulo,muhi]=[ 1.504e-01, 3.000e-01], [Flo,Fhi]=[ -0.0101, 0.0185]. it= 3: [mulo,muhi]=[ 1.504e-01, 2.252e-01], [Flo,Fhi]=[ -0.0101, 0.0075]. it= 4: [mulo,muhi]=[ 1.504e-01, 1.878e-01], [Flo,Fhi]=[ -0.0101, 0.0001]. it= 5: [mulo,muhi]=[ 1.691e-01, 1.878e-01], [Flo,Fhi]=[ -0.0045, 0.0001]. it= 6: [mulo,muhi]=[ 1.785e-01, 1.878e-01], [Flo,Fhi]=[ -0.0021, 0.0001]. it= 7: [mulo,muhi]=[ 1.831e-01, 1.878e-01], [Flo,Fhi]=[ -0.0010, 0.0001]. it= 8: [mulo,muhi]=[ 1.855e-01, 1.878e-01], [Flo,Fhi]=[ -0.0004, 0.0001]. it= 9: [mulo,muhi]=[ 1.866e-01, 1.878e-01], [Flo,Fhi]=[ -0.0002, 0.0001]. it=10: [mulo,muhi]=[ 1.872e-01, 1.878e-01], [Flo,Fhi]=[ -0.0000, 0.0001]. it=11: [mulo,muhi]=[ 1.872e-01, 1.875e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=12: [mulo,muhi]=[ 1.872e-01, 1.874e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=13: [mulo,muhi]=[ 1.873e-01, 1.874e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=14: [mulo,muhi]=[ 1.873e-01, 1.874e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=15: [mulo,muhi]=[ 1.873e-01, 1.873e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=16: [mulo,muhi]=[ 1.873e-01, 1.873e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=17: [mulo,muhi]=[ 1.873e-01, 1.873e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=18: [mulo,muhi]=[ 1.873e-01, 1.873e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. it=19: [mulo,muhi]=[ 1.873e-01, 1.873e-01], [Flo,Fhi]=[ -0.0000, 0.0000]. For corner of tradeoff curve use mu = 1.8734e-01. Then |(E,N)| equals 8.8877e-02, with lambda shown below: -2.1621e-01 1.6403e+00 9.6520e+00 7.0378e+00 -2.9271e+01 -8.3282e+01 -4.7069e-01 2.9740e+02 -2.0332e+02 Figure number 5 saved as cornfit.eps. Figure number 6 saved as cornerpt.eps.