t******g
发帖数: 1136 | 1 Suppose {x1, ..., xm} and {y1,..,yn} are two linear indepedent vector sets
in Hilbert space H, respectively. Suppose M = span{x1,..,xm},
N = span{y1,...,yn}. Suppose x \in H, and find the best approximation of x
in
M \cap N.
thank you ! | l******r
发帖数: 18699 | 2 suppose w is an m x n matrix such that
x_i=sum _j w_ij y_j, i=1,...,m
then M \cap N ={b_1 y_1+...+b_n y_n| a w=b has a solution in R^m}
so the problem is reduced to minimizing
||z-w'a|| over a \in R^m
given that z in R^n,where z is the vector of coefficients of an element in H
expaned by basis y
the best a=(ww')^- wz
()^- is the generalized inverse of a matrix
【在 t******g 的大作中提到】
: Suppose {x1, ..., xm} and {y1,..,yn} are two linear indepedent vector sets
: in Hilbert space H, respectively. Suppose M = span{x1,..,xm},
: N = span{y1,...,yn}. Suppose x \in H, and find the best approximation of x
: in
: M \cap N.
: thank you !
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