[討論] 統模第二題
power method那題
這題卡關好久啊
蔡丞庭的方法總讓我覺得怪怪的...
幸好有Google大神
讓我可以順利找到剩下的 那三個 害羞的 eigen vectors
大家可以參考下面這個網站
http://www.miislita.com/information-retrieval-tutorial/matrix-tutorial-3-
eigenvalues-eigenvectors.html#power-method
不會縮網址 將就一下
看The Power Method (Vector Iteration) 、The Deflation Method這兩個章節
應該就OK了
###########code 參考看看############
#Power Method
p.m = function(A,v=c(rep(1,nrow(A))),tol=10^-4){
w = c(rep(0,nrow(A)))
iter = 0
while( mean(abs(w-v)) >= tol){
w = v
v = A%*%v
b = sum(v^2)
v = v/sqrt(b)
iter = iter+1
}
list(value=sqrt(b),vector=v,iter=iter)
}
a1 = p.m(A) ; a1
## Deflation Method
Z = a1$value*a1$vector%*%t(a1$vector)
A2 = A - Z
a2 = p.m(A2) ; a2
#
Z2 = a2$value*a2$vector%*%t(a2$vector)
A3 = A2 - Z2
a3 = p.m(A3) ; a3
#
Z3 = a3$value*a3$vector%*%t(a3$vector)
A4 = A3 - Z3
a4 = p.m(A4) ; a4
--
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