Least Squares Approximations
When A x = b Ax=b Ax=b has no solutions , multiply by A T A^T AT and solve A T A x ^ = A T b A^TA\hat{x}=A^Tb ATAx^=ATb , x ^ \hat{x} x^ is least squares solution
例子:找一条最接近三个点(0,6),(1,0),(2,0)直线
如果存在一条直线 b=C+Dt 经过三个点,那么:
C + D ∗ 0 = 6 C + D ∗ 1 = 0 C + D ∗ 2 = 0 C+D*0=6\\ C+D*1=0\\ C+D*2=0 C+D∗0=6C+D∗1=0C+D∗2=0
写成矩阵形式:
[ 1 0 1 1 1 2 ] [ C D ] = [ 6 0 0