function?[QR]?=?grams（A）
%GRAMS??Gram-Schmidt?orthogonalization.
%???????[QR]?=?grams（A）?returns?matrix?Q?with?orthonormal
%???????columns?and?an?upper?triangular?R?so?that?Q*R?=?A.
%???????Warning:?this?algorithm?is?numerically?unstable.
%???????Use?MATLAB‘s?built-in?QR?function?for?stability.

[mn]?=?size（A）;
Asave?=?A;
for?j?=?1:n
???for?k?=?1:j-1
??????A（:j）?=?A（:j）?-?（A（:j）‘*A（:k））/（A（:k）‘*A（:k））*A（:k）;
???end
end
tol?=?1.e-6;
for?j?=?1:n
???if?norm（A（:j））???????error（‘Columns?are?linearly?dependent.‘）
???end
???Q（:j）?=?A（:j）/norm（A（:j））;
end
R?=?Q‘*Asave;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件????????802??2010-03-10?07:59??gramsmit.m

?????文件???????1081??2010-03-10?07:58??gs.m

?????文件????????610??2010-03-10?07:59??grams.m

-----------?---------??----------?-----??----

?????????????????2493????????????????????3