solution of 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
+ ... as many 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 ... set of equationsto be solved can bewritten as the N ×N set of equations
(A
T
· A) · x =(A
T
·b)(2.0.4)
where A
T
denotes the transpose of the matrix A. Equations (2.0.4) are called the
normal equations...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
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15/12/2013, 04:15
... case of N × 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 ... rows of A and the corresponding rows of the b’s
and of 1, does not change (or scramble in any way) the solution x’s and
Y. Rather, it just corresponds to writing the same set of linear equations
in ... 36
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 11 ppt
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15/12/2013, 04:15
... (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 page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... 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 ... America).
x[i]=sum/p[i];
}
}
A typicaluseof choldcand cholslis in theinversionof covariancematrices describing
the fit of data to a model; see, e.g., §15.6. In this, and many other applications,one often needs
L
−1
....
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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 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 ... modify the loop of the above fragment and (e.g.) divide by powers of ten,
to keep track of the scale separately, or (e.g.) accumulate the sum of logarithms of
the absolute values of the factors ... (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...
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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),
§
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
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 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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24/12/2013, 12:16
... 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 ... 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 so corrupted by roundoff error ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
Ngày tải lên :
24/12/2013, 12:16
... applications.)
• Each of the first 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 ... 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 ... also be aware of some of the special sparse forms that occur in the
solutionof partial differential equations in two or more dimensions. See Chapter 19.
If your particular pattern of sparsity is...
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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 0-521-43108-5)
Copyright ... 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),
§19. [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 ... root” of the matrix A.The
components of L
T
are of course related to those of L by
L
T
ij
= L
ji
(2.9.3)
Writing out equation (2.9.2) in components, one readily obtains the analogs of equations
(2.3.12)–(2.3.13),
L
ii
=
a
ii
−
i−1
k=1
L
2
ik
1/2
(2.9.4)
and
L
ji
=
1
L
ii
a
ij
−
i−1
k=1
L
ik
L
jk
j...
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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
... 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, ... 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, ... (PDAE),
nonnegative pencil of matrices, parallel method
1. Introduction
Recently there has been a growing interest in the analysis and numerical solution of PDAEs
because of their importance in various...
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- sceptical solution of these doubts
- the application of differential equations
- powerseries solution of odes
- systems of nonlinear equations
- systems of simultaneous equations
- solution of logic with vhdl
- applications of differential equations in physics
- applications of differential equations ppt
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