solution of simultaneous linear algebraic equations
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
+ ... equations as unknowns, and there is a good
chance of solving for a unique solution set of x
j
’s. Analytically, there can fail to
be a unique solution if one or more of the M equations is a linear ... 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 process....
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
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15/12/2013, 04:15
... of N ì N matrices, with M sets of right-hand
side vectors, in completely analogous fashion. The routine implemented below
is, of course, general.
38
Chapter 2. Solution of Linear Algebraic Equations
Sample ... 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
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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 ... solve the next set of linear equations. The LU
decomposition is complicated to update because of pivoting. However, QR turns out to be
quite simple for a very common kind of update,
A → A + s...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
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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 0-521-43108-5)
Copyright ... is called backsubstitution.Thecom-
bination of Gaussian elimination and backsubstitution yields a solution to the set
of equations.
The advantage of Gaussian elimination and backsubstitutionover ... York:
McGraw-Hill), 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...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
Ngày tải lên :
24/12/2013, 12:16
... 1967,
Computer 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 ... (i.e., selection of a salubrious pivot element
for the division in equation 2.3.13) is absolutely essential for the stability of Crout’s
50
Chapter 2. Solution of Linear Algebraic Equations
Sample ... (i=j;i<=n;i++) { This is i = j of equation (2.3.12) and i = j +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...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
Ngày tải lên :
24/12/2013, 12:16
... 1967,
Computer 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 0-521-43108-5)
Copyright ... 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 0-521-43108-5)
Copyright...
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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 0-521-43108-5)
Copyright ... submatrices. Imagine doing the inversionof a very large matrix, of order
N =2
m
, recursively by partitions in half. At each step, halving the order doubles
the number of inverse operations. But this ... complicated nature
of the recursive Strassen algorithm, you will find that LU decomposition is in no
immediate danger of becoming obsolete.
If, on the other hand, you like this kind of fun, then try...
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Tài liệu Solution of Linear Algebraic Equations part 6 pptx
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... improved solution x.
2.5 Iterative Improvement of a Solution to
Linear Equations
Obviously it is not easy to obtain greater precision for the solution of a linear
set than the precision of your ... 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 0-521-43108-5)
Copyright ... Proceedings of the Seventeenth Annual ACM Symposium on
Theory of Computing (New York: Association for Computing Machinery). [1]
2.5 Iterative Improvement of a Solution to Linear Equations
57
Sample...
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Tài liệu Solution of Linear Algebraic Equations part 7 docx
Ngày tải lên :
24/12/2013, 12:16
... North America).
A
⋅
x = b
SVD solution
of A
⋅
x = c
solutions of
A
⋅
x = c′
solutions of
A
⋅
x = d
null
space
of A
SVD solution of
A
⋅
x = d
range of A
d
c
(b)
(a)
A
x
b
c′
Figure ... making
the same permutation of the columns of U,elementsofW,andcolumnsofV(or
rows of V
T
), or (ii) forming linear combinations of any columns of U and V whose
corresponding elements of W happen to be ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
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... case of a tridiagonal matrix was treated specially, because that
particular type of linear system admits a solution in only of order N operations,
rather than of order N
3
for the general linear ... form the sequence of improved estimates
x
k+1
= x
k
+ α
k
p
k
(2.7.37)
76
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... applications.)
ã Each of the rst N locations of ija stores the index of the array sa that contains
the first off-diagonal element of the corresponding row of the matrix. (If there are
no off-diagonal elements...
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Tài liệu Solution of Linear Algebraic Equations part 9 docx
Ngày tải lên :
21/01/2014, 18:20
... case of a tridiagonal matrix was treated specially, because that
particular type of linear system admits a solution in only of order N operations,
rather than of order N
3
for the general linear ... 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 0-521-43108-5)
Copyright ... 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 0-521-43108-5)
Copyright...
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Tài liệu Solution of Linear Algebraic Equations part 10 docx
Ngày tải lên :
21/01/2014, 18:20
... 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 ... for fast solution of the symmetric Toeplitz problem, by a bordering method,thatis,
98
Chapter 2. Solution of Linear Algebraic Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... case of a tridiagonal matrix was treated specially, because that
particular type of linear system admits a solution in only of order N operations,
rather than of order N
3
for the general linear...
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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
... the 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, ... 263.
VNU Journal of Science, Mathematics - Physics 23 (2007) 201-209
Fully parallel methods for a class of linear partial
differential -algebraic equations
Vu Tien Dung
∗
Department of Mathematics, ... [3].
Discretizing the BVP (12)-(13) one obtains a large-scale system of linear equations
Lw = g, (19)
where L is a symmetric positive define matrix of dimension p ì p, where p = p(h) depends on the
discretization...
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