octave:2> m=9 m = 9 octave:3> x=linspace(0,1,m)'; octave:4> epsilon=1/4 epsilon = 0.25000 octave:5> (1/2-epsilon <= x & x < 1/2+epsilon) ans = 0 0 1 1 1 1 0 0 0 octave:6> fem0 octave:7> uesatta-uhat ans = 4.3368e-19 -4.5103e-17 -9.0206e-17 -1.3878e-16 -1.8041e-16 -2.2204e-16 -2.7756e-16 -3.0531e-16 -3.0531e-16 -3.6082e-16 -3.8858e-16 -4.4409e-16 -4.9960e-16 -4.9960e-16 -4.9960e-16 -4.7184e-16 -3.8858e-16 -3.0531e-16 -2.0817e-16 -1.0755e-16 4.3368e-19 octave:8> fem0 octave:9> fem0 octave:10> fem0 octave:11> g g = 0.00000 0.00000 -0.12500 -0.25000 -0.25000 -0.25000 -0.12500 0.00000 0.00000 octave:12> fem0 warning: matrix singular to machine precision, rcond = 0 warning: attempting to find minimum norm solution octave:13> fem0 octave:14> cond(A) ans = 1.4625e+19 octave:15> 2^60 ans = 1.1529e+18 octave:16> fem0 octave:17> fem0 warning: matrix singular to machine precision, rcond = 0 warning: attempting to find minimum norm solution octave:18> cond(A) ans = 3.9660e+16 octave:19> v=[1+1i;2-2i] v = 1 + 1i 2 - 2i octave:20> v' ans = 1 - 1i 2 + 2i octave:21> v.' ans = 1 + 1i 2 - 2i octave:22> fourier octave:23> plot(x,u) octave:24> u u = 0.56111 + 0.00000i 0.56501 + 0.00000i 0.56896 - 0.00000i 0.57294 + 0.00000i 0.57696 - 0.00000i 0.58101 - 0.00000i 0.58509 + 0.00000i 0.58920 + 0.00000i 0.59334 - 0.00000i 0.59751 - 0.00000i 0.60169 - 0.00000i 0.60590 - 0.00000i 0.61012 + 0.00000i 0.61435 - 0.00000i 0.61859 - 0.00000i 0.62284 + 0.00000i 0.62709 - 0.00000i 0.63134 - 0.00000i 0.63559 + 0.00000i 0.63983 + 0.00000i 0.64406 - 0.00000i 0.64827 - 0.00000i 0.65246 - 0.00000i 0.65663 - 0.00000i 0.66077 + 0.00000i 0.66488 - 0.00000i 0.66895 - 0.00000i 0.67298 + 0.00000i 0.67697 - 0.00000i 0.68090 - 0.00000i 0.68478 + 0.00000i 0.68859 + 0.00000i 0.69234 - 0.00000i 0.69602 - 0.00000i 0.69963 - 0.00000i 0.70315 - 0.00000i 0.70659 - 0.00000i 0.70993 - 0.00000i 0.71318 - 0.00000i 0.71633 - 0.00000i 0.71937 - 0.00000i 0.72230 - 0.00000i 0.72512 - 0.00000i 0.72781 + 0.00000i 0.73038 - 0.00000i 0.73282 + 0.00000i 0.73512 - 0.00000i 0.73728 - 0.00000i 0.73930 + 0.00000i 0.74118 - 0.00000i 0.74290 + 0.00000i 0.74447 - 0.00000i 0.74588 - 0.00000i 0.74714 - 0.00000i 0.74823 - 0.00000i 0.74916 - 0.00000i 0.74992 - 0.00000i 0.75051 + 0.00000i 0.75094 - 0.00000i 0.75119 - 0.00000i 0.75128 - 0.00000i 0.75119 - 0.00000i 0.75094 + 0.00000i 0.75051 - 0.00000i 0.74992 - 0.00000i 0.74916 - 0.00000i 0.74823 - 0.00000i 0.74714 - 0.00000i 0.74588 - 0.00000i 0.74447 + 0.00000i 0.74290 - 0.00000i 0.74118 - 0.00000i 0.73930 + 0.00000i 0.73728 - 0.00000i 0.73512 + 0.00000i 0.73282 - 0.00000i 0.73038 - 0.00000i 0.72781 - 0.00000i 0.72512 - 0.00000i 0.72230 - 0.00000i 0.71937 + 0.00000i 0.71633 + 0.00000i 0.71318 - 0.00000i 0.70993 + 0.00000i 0.70659 - 0.00000i 0.70315 - 0.00000i 0.69963 + 0.00000i 0.69602 - 0.00000i 0.69234 - 0.00000i 0.68859 - 0.00000i 0.68478 - 0.00000i 0.68090 - 0.00000i 0.67697 + 0.00000i 0.67298 + 0.00000i 0.66895 - 0.00000i 0.66488 + 0.00000i 0.66077 + 0.00000i 0.65663 - 0.00000i 0.65246 + 0.00000i 0.64827 + 0.00000i 0.64406 + 0.00000i 0.63983 - 0.00000i 0.63559 + 0.00000i 0.63134 - 0.00000i 0.62709 + 0.00000i 0.62284 - 0.00000i 0.61859 + 0.00000i 0.61435 + 0.00000i 0.61012 + 0.00000i 0.60590 - 0.00000i 0.60169 + 0.00000i 0.59751 + 0.00000i 0.59334 + 0.00000i 0.58920 - 0.00000i 0.58509 + 0.00000i 0.58101 - 0.00000i 0.57696 + 0.00000i 0.57294 - 0.00000i 0.56896 + 0.00000i 0.56501 + 0.00000i 0.56111 + 0.00000i 0.55725 + 0.00000i 0.55343 - 0.00000i 0.54966 + 0.00000i 0.54593 + 0.00000i 0.54225 - 0.00000i 0.53862 + 0.00000i 0.53505 - 0.00000i 0.53152 + 0.00000i 0.52805 - 0.00000i 0.52464 + 0.00000i 0.52128 + 0.00000i 0.51798 + 0.00000i 0.51474 + 0.00000i 0.51155 - 0.00000i 0.50843 + 0.00000i 0.50537 + 0.00000i 0.50236 - 0.00000i 0.49942 + 0.00000i 0.49655 - 0.00000i 0.49374 + 0.00000i 0.49099 - 0.00000i 0.48830 + 0.00000i 0.48569 + 0.00000i 0.48313 + 0.00000i 0.48065 + 0.00000i 0.47823 - 0.00000i 0.47587 + 0.00000i 0.47359 + 0.00000i 0.47137 - 0.00000i 0.46922 + 0.00000i 0.46714 - 0.00000i 0.46513 + 0.00000i 0.46319 - 0.00000i 0.46131 + 0.00000i 0.45951 + 0.00000i 0.45777 - 0.00000i 0.45611 + 0.00000i 0.45451 - 0.00000i 0.45299 - 0.00000i 0.45153 + 0.00000i 0.45015 + 0.00000i 0.44884 - 0.00000i 0.44759 - 0.00000i 0.44642 + 0.00000i 0.44532 + 0.00000i 0.44429 + 0.00000i 0.44332 + 0.00000i 0.44244 + 0.00000i 0.44162 + 0.00000i 0.44087 - 0.00000i 0.44019 - 0.00000i 0.43959 + 0.00000i 0.43905 + 0.00000i 0.43859 - 0.00000i 0.43820 - 0.00000i 0.43788 + 0.00000i 0.43763 + 0.00000i 0.43745 + 0.00000i 0.43734 + 0.00000i 0.43731 - 0.00000i 0.43734 + 0.00000i 0.43745 - 0.00000i 0.43763 - 0.00000i 0.43788 + 0.00000i 0.43820 + 0.00000i 0.43859 - 0.00000i 0.43905 + 0.00000i 0.43959 + 0.00000i 0.44019 + 0.00000i 0.44087 + 0.00000i 0.44162 + 0.00000i 0.44244 + 0.00000i 0.44332 + 0.00000i 0.44429 + 0.00000i 0.44532 - 0.00000i 0.44642 + 0.00000i 0.44759 + 0.00000i 0.44884 - 0.00000i 0.45015 + 0.00000i 0.45153 + 0.00000i 0.45299 + 0.00000i 0.45451 + 0.00000i 0.45611 + 0.00000i 0.45777 - 0.00000i 0.45951 + 0.00000i 0.46131 + 0.00000i 0.46319 - 0.00000i 0.46513 + 0.00000i 0.46714 + 0.00000i 0.46922 - 0.00000i 0.47137 + 0.00000i 0.47359 - 0.00000i 0.47587 + 0.00000i 0.47823 + 0.00000i 0.48065 - 0.00000i 0.48313 + 0.00000i 0.48569 + 0.00000i 0.48830 + 0.00000i 0.49099 + 0.00000i 0.49374 - 0.00000i 0.49655 + 0.00000i 0.49942 + 0.00000i 0.50236 + 0.00000i 0.50537 - 0.00000i 0.50843 - 0.00000i 0.51155 - 0.00000i 0.51474 - 0.00000i 0.51798 + 0.00000i 0.52128 + 0.00000i 0.52464 - 0.00000i 0.52805 + 0.00000i 0.53152 - 0.00000i 0.53505 + 0.00000i 0.53862 + 0.00000i 0.54225 + 0.00000i 0.54593 - 0.00000i 0.54966 - 0.00000i 0.55343 - 0.00000i 0.55725 - 0.00000i octave:25> format long e octave:26> u u = 5.61108547462738e-01 + 0.00000000000000e+00i 5.65012395816921e-01 + 6.97462535450211e-19i 5.68956250504707e-01 - 1.03808048906885e-18i 5.72938150612176e-01 + 3.46027269686044e-19i 5.76956040980257e-01 - 1.03862241066755e-17i 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5.08428826874573e-01 - 2.12506264667370e-19i 5.11552886792403e-01 - 2.75907372223525e-18i 5.14736935105413e-01 - 6.22986797019048e-18i 5.17980095428800e-01 + 6.21595978452066e-35i 5.21281437420584e-01 + 2.62855902240362e-18i 5.24639974352921e-01 - 3.00879497526230e-19i 5.28054660627522e-01 + 1.72260375513811e-19i 5.31524389237761e-01 - 6.30315584264193e-18i 5.35047989180554e-01 + 8.79970588092408e-19i 5.38624222821619e-01 + 8.39825825079517e-19i 5.42251783218344e-01 + 1.31471335736774e-17i 5.45929291405107e-01 - 1.07252828353770e-17i 5.49655293646623e-01 - 4.52781024301977e-19i 5.53428258665660e-01 - 6.36351239749592e-18i 5.57246574852288e-01 - 9.47468940946921e-18i octave:27> g g = @(x) 1 ./ (sin (x) + 2) octave:28> x x = -3.14159265358979e+00 -3.11541271480988e+00 -3.08923277602996e+00 -3.06305283725005e+00 -3.03687289847013e+00 -3.01069295969022e+00 -2.98451302091030e+00 -2.95833308213039e+00 -2.93215314335047e+00 -2.90597320457056e+00 -2.87979326579064e+00 -2.85361332701073e+00 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5.47027969043087e-16i 4.65982470437745e-16 + 4.80735243280073e-16i -1.72604985859692e-16 - 1.81548976156340e-15i -5.71184809519676e-16 - 2.42861286636753e-16i 9.78384040450919e-16 + 5.03286648467771e-16i 1.51788304147971e-17 + 2.22044604925031e-16i 2.22044604925031e-16 - 5.89805981832114e-17i 1.01654795692241e-15 - 8.88178419700125e-16i 0.00000000000000e+00 - 5.13478148889135e-16i -1.79023462720806e-15 - 0.00000000000000e+00i octave:37> sqrt(h*sum(g(x).^2)) ans = 1.55512030155621e+00 octave:38> norm(ghat) ans = 1.48896777456336e+02 octave:39> norm(ghat)*sqrt(2*pi)/m ans = 1.55512030155621e+00 octave:40> diary off