Conditionarea matricei lui Hilbert
Calculeaza conditionarea matricei Hilbert cu ajutorul valorilor proprii. Se va utiliza formula
O estimare teoretica, pentru mare, datorata lui Szego, este
format short e for n=[10:10:100] c = max(eig(hilb(n)))*max(eig(invhilb(n))); th = (sqrt(2)+1)^(4*n+4)/(2^(15/4)*sqrt(pi*n)); fprintf('%3d, %11.4e, %11.4e\n', n,c,th) end
10, 1.6026e+13, 9.2192e+14 20, 2.4522e+28, 1.3342e+30 30, 4.2278e+43, 2.2294e+45 40, 7.6529e+58, 3.9513e+60 50, 1.4229e+74, 7.2330e+75 60, 2.6913e+89, 1.3513e+91 70, 5.1508e+104, 2.5604e+106 80, 9.9444e+119, 4.9016e+121 90, 1.9328e+135, 9.4578e+136 100, 3.7765e+150, 1.8363e+152