Matlab 向量相乘问题

Question

矩阵D_z = [722483478143.668,59820245325.4305,-4908044696.28673,8066748023.31476,588289266.823277,-586279368239.143;52871956232.2195,6443869298.76580,-361209979.771828,588289266.823276,85273557.8932953,-43113851863.2673;52510058821062.8,4365173390310.01,-356718832131.733,586279368239.143,43113851863.2674,-42611619281260.0;64708490769470.8,5366654578526.81,-439586953542.062,722483478143.667,52871956232.2196,-52510058821062.8;5366654578526.80,545841409946.368,-36556661167.5860,59820245325.4304,6443869298.76581,-4365173390310.01;439586953542.062,36556661167.5861,-2986197833.74336,4908044696.28673,361209979.771828,-356718832131.733]
R_0 =[4.98336244340045e-05;5.22560769642106e-06;-0.00771970922989240;0;0;0.000126569771011181]
R_z = D_z*R_0
计算结果为R_z =[7.89963929138611e-09;-5.21738246578461e-11;1.83363302230939e-07;-6.57502726960382e-08;4.25865463971400e-08;-1.05253038136285e-08]
可是当我用 D_z(1,:)*R_0 时 ans=1.490116119384766e-08 不等于R_z(1)啊 什么情况

Answer 1

数值误差的影响，矩阵相称数值量级相差太大，造成了误差，若要解决此问题，计算时使用符号量代替数值量，如下：

format long
D_z = [722483478143.668,59820245325.4305,-4908044696.28673,8066748023.31476,588289266.823277,-586279368239.143;52871956232.2195,6443869298.76580,-361209979.771828,588289266.823276,85273557.8932953,-43113851863.2673;52510058821062.8,4365173390310.01,-356718832131.733,586279368239.143,43113851863.2674,-42611619281260.0;64708490769470.8,5366654578526.81,-439586953542.062,722483478143.667,52871956232.2196,-52510058821062.8;5366654578526.80,545841409946.368,-36556661167.5860,59820245325.4304,6443869298.76581,-4365173390310.01;439586953542.062,36556661167.5861,-2986197833.74336,4908044696.28673,361209979.771828,-356718832131.733]
R_0 =[4.98336244340045e-05;5.22560769642106e-06;-0.00771970922989240;0;0;0.000126569771011181]
R_z = sym(D_z)*sym(R_0);

R1 = R_z(1)
R2 = sym(D_z(1,:))*sym(R_0) 

R1s = double(R1)
R2s = double(R2)

结果：

R1 =
 
10952043364488277297/77371252455336267181195264
 
 
R2 =
 
10952043364488277297/77371252455336267181195264
 

R1s =

     1.415518427960115e-07


R2s =

     1.415518427960115e-07