Tài liệu Solution of Linear Algebraic Equations part 1 docx
Tài liệu Solution of Linear Algebraic Equations part 1 docx
... Introduction
A set of linear algebraic equations looks like this:
a
11
x
1
+ a
12
x
2
+ a
13
x
3
+ ···+a
1N
x
N
=b
1
a
21
x
1
+ a
22
x
2
+ a
23
x
3
+ ···+a
2N
x
N
=b
2
a
31
x
1
+ a
32
x
2
+ a
33
x
3
+ ···+a
3N
x
N
=b
3
··· ... call 1- 800-872-7423 (North America only),or send email to trade@cup.cam.ac.uk (outside North America).
Chapter 2. Solution of Linear...
Tài liệu Solution of Linear Algebraic Equations part 4 docx
... above). For the case of
a 4 × 4 matrix A, for example, equation (2.3 .1) would look like this:
α
11
000
α
21
α
22
00
α
31
α
32
α
33
0
α
41
α
42
α
43
α
44
·
β
11
β
12
β
13
β
14
0 β
22
β
23
β
24
00β
33
β
34
000β
44
=
a
11
a
12
a
13
a
14
a
21
a
22
a
23
a
24
a
31
a
32
a
33
a
34
a
41
a
42
a
43
a
44
(2.3.2)
We ... α
ii
(equation 2.3 .11 ) are...
Tài liệu Solution of Linear Algebraic Equations part 5 docx
... in
a [1 n][m1 +1]
. Subdiagonal elements are in
a[
j
n] [1 m1]
(with j>1ap-
propriate to the number of elements on each subdiagonal). Superdiagonal elements are in
a [1
j
][m1+2 m1+m2 +1]
with ... The set of equations to be solved is
b
1
c
1
0 ···
a
2
b
2
c
2
···
···
··· a
N 1
b
N 1
c
N 1
··· 0 a
N
b
N
·
u
1
u
2
···
u
N 1
u
N
=...
Tài liệu Solution of Linear Algebraic Equations part 7 docx
... N
(2.6.2)
N
j =1
V
jk
V
jn
= δ
kn
1 ≤ k ≤ N
1 ≤ n ≤ N
(2.6.3)
68
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)
Copyright ... {
z =1. 0/z;
c=f*z;
s=h*z;
}
f=c*g+s*y;
x=c*y-s*g;
70
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES...
Tài liệu Solution of Linear Algebraic Equations part 8 docx
... ⊗v)
1
, and is derived
briefly as follows:
(A + u ⊗ v)
1
= (1+ A
1
·u⊗v)
1
·A
1
= (1 A
1
·u⊗v+A
1
·u⊗v·A
1
·u⊗v− )·A
1
=A
1
−A
1
·u⊗v·A
1
(1 − λ + λ
2
− )
=A
1
−
(A
1
·u)⊗(v·A
1
)
1+ λ
(2.7.2)
where
λ ... =(P−Q·S
1
·R)
1
Q=−(P−Q·S
1
·R)
1
·(Q·S
1
)
R=−(S
1
·R)·(P−Q·S
1
·R)
1
S=S
1
+(S
1
·R)·(P−Q·S
1
·R)
1
·(Q·S
1
)
(2.7.24)
or els...
Tài liệu Solution of Linear Algebraic Equations part 9 docx
... )
j
− G
(M +1)
M +1
H
(M )
M +1 j
H
(M +1)
j
= H
(M )
j
− H
(M +1)
M +1
G
(M )
M +1 j
(2.8.25)
Now, starting with the initial values
x
(1)
1
= y
1
/R
0
G
(1)
1
= R
1
/R
0
H
(1)
1
= R
1
/R
0
(2.8.26)
we ... +1)
j
x
(M +1)
M +1
= R
i−(M +1)
i =1, ,M (2.8 .13 )
or by letting i → M +1 i and j → M +1 j,
M
j =1
R
j−i
G
(M )
j
= R
−i
(2.8 .14 )
where
G
(M)
j
≡
x
(M)
M +1...
Tài liệu Solution of Linear Algebraic Equations part 10 docx
... )
j
− G
(M +1)
M +1
H
(M )
M +1 j
H
(M +1)
j
= H
(M )
j
− H
(M +1)
M +1
G
(M )
M +1 j
(2.8.25)
Now, starting with the initial values
x
(1)
1
= y
1
/R
0
G
(1)
1
= R
1
/R
0
H
(1)
1
= R
1
/R
0
(2.8.26)
we ... +1)
j
x
(M +1)
M +1
= R
i−(M +1)
i =1, ,M (2.8 .13 )
or by letting i → M +1 iand j → M +1 j,
M
j =1
R
j−i
G
(M )
j
= R
−i
(2.8 .14 )
where
G
(M)
j
≡
x
(M)
M +1...
Tài liệu Solution of Linear Algebraic Equations part 2 ppt
... x:
A · x = b
A · C
1
· C
1
1
· x = b
A · C
1
· C
2
· C
1
2
· C
1
1
· x = b
(A · C
1
· C
2
· C
3
···)···C
1
3
·C
1
2
·C
1
1
·x =b
(1) ···C
1
3
·C
1
2
·C
1
1
·x =b
(2 .1. 7)
... equation
a
11
a
12
a
13
a
14
a
21
a
22
a
23
a
24
a
31
a
32
a
33
a
34
a
41
a
42
a
43
a
44
·
x
11
x
21
x
31
x
41
x
12
x
22
x
32
x
42
x...
Tài liệu Solution of Linear Algebraic Equations part 11 ppt
... solve linear systems. In many applications only the
part (2 .10 .4) of the algorithm is needed, so we separate it off into its own routine rsolv.
10 0
Chapter 2. Solution of Linear Algebraic Equations
Sample ... 98
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)
Cop...
Tài liệu Solution of Linear Algebraic Equations part 3 pdf
... elimination.
42
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-5 21- 4 310 8-5)
Copyright (C) 19 88 -19 92 by Cambridge University ... (in the case of a single right-hand side vector):
a
11
a
12
a
13
a
14
0 a
22
a
23
a
24
00a
33
a
34
000a
44
·
x
1...