Page 39 - Compact Numerical Methods For Computers

Formal problems in linear algebra 29
the dimensions of the system. If a linear combination of some functions f ,
i
j = 1, 2, . . . ) n, is used for F, that is

(2.66)

then the variation method gives rise to the eigenvalue problem
Ax = eBx (2.63)
with
A ij = (f , Hf ) (2.67)
j
i
and
B ij = (f , f ) (2.68)
i
j
It is obvious that if B is a unit matrix, that is, if
(f , f ) = d = { 1 for i = j (2.69)
0
for i j
i
i
ij
a problem of type (2.56) arises. A specific example of such a problem is equation
(11.1).