K Kp
<p 1) ts
25
usual one as regards operational counts. The indices-calculus will
show its advantage in this matter as well.
The steps are:
Usual
a. e" g«3 up Kp.
New
gag Mp yoc ^P_
b. gag ut> uo
0 a 3
number: each consis-
2
For replacing this set of equa
tions the same number of coeffi
cients is needed.
ting of the sum of a products.
c. Solution of p normal-equa
tions: - (P 2) pro.
6
To obtain the new coefficients
US are neededin all the sum of
(a 1) products;
2
p(p 1)
- - divisions, and for the
2
ducts and p I) divisions.
2
solution of G?" Kp =te p divi
sions.
d. Substituting Kp in I.
e. Solution of the set:
GptI0
Additional to c:
6
Calculating the reciprocals of
Gee p divisions.
f. tensor of cofactors
a (a -f i)
number: each con-
2
ditto
a (a 1)
number: each con-
sisting of the sum of p2 products.
sisting of the sum of p products.
The differences occur under c, e, and f. The additional work
under c of the new method is very slight compared with the ad
vantage of e and f. In the last step the proportion is p2 p. In this
case the orthogonalization-methodand diagonalizing the matrix
of the normal-equations is preferable to the orthodox method of
calculation.
M See e.g. Alston S. Householder "Principles of Numerical Analysis" Ed.
Mc Graw-Hill book cy. inc. 1953.
