solving linear algebraic equations using matlab
Tài liệu Solution of Linear Algebraic Equations part 1 docx
Ngày tải lên :
15/12/2013, 04:15
... trade@cup.cam.ac.uk (outside North America).
Chapter 2. Solution of Linear
Algebraic Equations
2.0 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
+ ... overdetermined linear problem reduces to
a (usually) solvable linear problem, called the
ã Linear least-squares problem.
Thereduced set of equationsto be solved can bewritten as the N ìN set of equations
(A
T
à ... sophistication of complicated linear equation -solving packages”
is devoted to the detection and/or correction of these two pathologies. As you
work with large linear sets of equations, you will develop...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
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15/12/2013, 04:15
... elimination is about as efficient as any
other method. For solving sets of linear equations, Gauss-Jordan elimination
produces both the solution of the equations for one or more right-hand side vectors
b, ... and Moler, C.B. 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall).
Wilkinson, J.H., and Reinsch, C. 1971,
Linear Algebra
,vol.IIof
Handbook for Automatic ... 36
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
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15/12/2013, 04:15
... not used for typical systems of linear equations. However, we will
meet special cases where QR is the method of choice.
100
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL ... 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.
98
Chapter 2. Solution of Linear Algebraic Equations
Sample ... numericalalgorithms involve solvinga successionof linear systems each of which
differs only slightly from its predecessor. Instead of doing O(N
3
) operations each time
to solve the equations from scratch,...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
Ngày tải lên :
24/12/2013, 12:16
... 42
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... Program B-2, p. 298.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York: Wiley).
Ralston, A., and Rabinowitz, P. 1978,
A First Course in Numerical ... containing one subtraction and
one multiplication, are executed N
3
and N
2
M times (where there are N equations
and M unknowns). The corresponding loops in Gaussian elimination are executed
only
1
3
N
3
times...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
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24/12/2013, 12:16
... solve the linear set
A · x =(L·U)·x=L·(U·x)=b (2.3.3)
by first solving for the vector y such that
L · y = b (2.3.4)
and then solving
U · x = y (2.3.5)
What is the advantage of breaking up one linear ... Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New ... a
ij
(2.3.10)
Equations (2.3.8)–(2.3.10) total N
2
equations for the N
2
+ N unknown α’s and
β’s (the diagonal being represented twice). Since the number of unknowns is greater
than the number of equations, ...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
Ngày tải lên :
24/12/2013, 12:16
... Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall), Chapters 9, 16, and 18.
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New ... (j=LMAX(1,1-k);j<=tmploop;j++) b[i] += a[i][j]*x[j+k];
}
}
54
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... 2nd ed. (Baltimore: Johns Hopkins
University Press),
Đ
4.3.
50
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...
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Tài liệu Solution of Linear Algebraic Equations part 12 pdf
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24/12/2013, 12:16
... 104
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... 1987,
Algorithms: Their Complexity and Efciency
, 2nd ed. (New York: Wiley).
Winograd, S. 1971,
Linear Algebra and Its Applications
, vol. 4, pp. 381–388.
Pan, V. Ya. 1980,
SIAM Journal on Computing
, ... inverses of each other. Then the c’s can be obtained from the a’s by the following
operations (compare equations 2.7.22 and 2.7.25):
R
1
= Inverse(a
11
)
R
2
= a
21
ì R
1
R
3
= R
1
ì a
12
R
4
= a
21
ì...
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Tài liệu Solution of Linear Algebraic Equations part 6 pptx
Ngày tải lên :
24/12/2013, 12:16
... 56
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... enough; but a second
call to verify convergence can be reassuring.
58
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... δb. The linear set with this right-hand
side is inverted, giving δx. This is subtracted from the first guess giving an improved solution x.
2.5 Iterative Improvement of a Solution to
Linear Equations
Obviously...
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Tài liệu Solution of Linear Algebraic Equations part 7 docx
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24/12/2013, 12:16
... Sparse Linear Systems
A system of linear equations is called sparse if only a relatively small number
of its matrix elements a
ij
are nonzero. It is wasteful to use general methods of
linear ... throwing away one linear combination of the set of equations that
we are trying to solve. The resolution of the paradox is that we are throwing away
precisely a combination of equations that is ... *g;
g=s=scale=0.0;
if(i<=m&&i!=n){
for (k=l;k<=n;k++) scale += fabs(a[i][k]);
if (scale) {
62
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN...
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Electronics and Circuit Analysis Using MATLAB P1
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...
MATLAB has a rich set of plotting capabilities. The graphics are integrated in
MATLAB. Since MATLAB is also a programming environment, a user can
extend the functional capabilities of MATLAB ...
1.1 MATLAB BASIC OPERATIONS
When MATLAB is invoked, the command window will display the prompt >>.
MATLAB is then ready for entering data or executing commands. To quit
MATLAB, ... 21 elements using 168 bytes.
Table 1.2 shows additional MATLAB commands to get one started on
MATLAB. Detailed descriptions and usages of the commands can be obtained
from the MATLAB help...
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