Beispiel - SAM - ETH Zürich

g i = y 0 +h s ∑
j=1
a ij f(g j ) ➣ k i = f(g i ),i = 1,...,s, y 0 = g i −h s ∑
j=1
a ij f(g j ).
Numerische
Mathemtik
Einsetzen in (4.1.9), da aus (4.1.8) folgt g i Mf(g i ) = 0:
y T 1 My 1−y T 0 My 0 = 2h
s∑
i=1
b i
⎛
⎝g i −h
⎞
s∑
a ij f(g j ) ⎠
j=1
= −2h 2 ∑ s s∑
b i a ij f(g j ) T Mf(g i )+h 2 ∑ s
i=1
j=1
T
Mf(g i )+h 2 s ∑
i=1
= h 2 s ∑
i=1
i=1
s∑
b i b j f(g i ) T Mf(g j )
j=1
s∑
b i b j f(g i ) T Mf(g j )
j=1
s∑
(−2b i a ij +b i b j )f(g i ) T Mf(g j ) .
j=1
R. Hiptmair
rev 35327,
24. Juni
2011
M = M T ➣ Indexvertauschung in der Doppelsumme ➣ Behauptung. ✷
4.1
p. 442