solve linear algebraic equations 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 ... linear combinations of each other, some of the equations
may be so close to linearly dependent that roundoff errors in the machine
render them linearly dependent at some stage in the solution...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
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15/12/2013, 04:15
... 36
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... 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 ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
Ngày tải lên :
15/12/2013, 04:15
... to 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 ... SVD, Cholesky), QR decompo-
sition can be used to solve systems of linear equations. To solve
A · x = b (2.10.3)
first form Q
T
· b and then solve
R · x = Q
T
· b (2.10.4)
by backsubstitution. ... 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...
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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 ... backsubstitution.Thecom-
bination of Gaussian elimination and backsubstitution yields a solution to the set
of equations.
The advantage of Gaussian elimination and backsubstitutionover Gauss-Jordan
elimination...
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Tài liệu Solution of Linear Algebraic Equations part 4 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 ... substitution and backsubstitution,implementing
equations (2.3.6) and (2.3.7).
void lubksb(float **a, int n, int *indx, float b[])
Solves the set of
n
linear equations A·X = B.Here
a[1 n][1 n]
is input, ... +1 N
of equation (2.3.13).sum=a[i][j];
for (k=1;k<j;k++)
44
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 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 ... arrays
a
,
al
,and
indx
as returned from
bandec
, and given a right-hand side vector
b[1 n]
, solves the band diagonal linear equations A · x = b. The solution vector x overwrites
b[1 n]
. The other input arrays...
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Tài liệu Solution of Linear Algebraic Equations part 12 pdf
Ngày tải lên :
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
Ngày tải lên :
24/12/2013, 12:16
... 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 ... we wish to find the least-squares
solution to an overdetermined set of linear equations. In tableau, the equations
to be solved are
A
·
x
=
b
(2.6.11)
The ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
Ngày tải lên :
24/12/2013, 12:16
... general
routine, linbcg below, that solves the set of linear equations, (2.7.29), using your functions.
The simplest, “ordinary” conjugategradient algorithm
[11-13]
solves (2.7.29) only in the
casethatAis ... 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 ... transpose on a vector; and
asolve
, which solves
A ·x = b or
A
T
·x = b for some preconditioner matrix
A (possibly the trivial diagonal part of A).
{
void asolve(unsigned long n, double...
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Tài liệu Solution of Linear Algebraic Equations part 9 docx
Ngày tải lên :
21/01/2014, 18:20
... 92
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... always to compute Vandermonde
problems in double precision.
94
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... Levinson’s method. These methods are too complicated to include here.
90
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 10 docx
Ngày tải lên :
21/01/2014, 18:20
... SVD, Cholesky), QR decompo-
sition can be used to solve systems of linear equations. To solve
A · x = b (2.10.3)
first form Q
T
· b and then solve
R · x = Q
T
· b (2.10.4)
by backsubstitution. ... used to solve a linear
equation by backsubstitution. The straightforward implementation of this is
void cholsl(float **a, int n, float p[], float b[], float x[])
Solves the set of
n linear equations ... 1967,
Computer Solution of Linear Algebraic Systems
(Engle-
wood Cliffs, NJ: Prentice-Hall),
Đ19. [1]
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York:...
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Tài liệu Báo cáo " Fully parallel methods for a class of linear partial differential-algebraic equations " pptx
Ngày tải lên :
13/02/2014, 03:20
... Solution of Linear Parabolic Problems, Applied Mathematics Research Express No. 4
(2005) 117.
[5] R.D. da Cunha, T.R. Hopkins, Parallel Over Relaxation Algorithms for Systems of Linear Equations, ... Mathematics - Physics 23 (2007) 201-209
Fully parallel methods for a class of linear partial
differential -algebraic equations
Vu Tien Dung
∗
Department of Mathematics, Mechanics, Informatics, College ... December 2007
Abstract. This note deals with two fully parallel methods for solving linear partial differential-
algebraic equations (PDAEs) of the form:
Au
t
+ B∆u = f(x, t) (1)
where A is a singular,...
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