solution of nonlinear algebraic equations matlab
Tài liệu Solution of Linear Algebraic Equations part 1 docx
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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 ìN set of equations
(A
T
à A) à x =(A
T
Ãb)(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
... 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 ... 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., Đ15.6. 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),
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
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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
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24/12/2013, 12:16
... 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 ... 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
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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),
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 ... 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 Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
Ngày tải lên :
19/02/2014, 22:20
... collection of events, sigma-algebra
A
filtration
E(X) expectation of X
E(X |A) conditional expectation of X under A
P (A) probability of A
P (A |B) probability of A conditioned on B
∈ element of
∈ ... approxi-
mation of continuous solutions of SDEs. The discrete time approximation of
SDEs with jumps represents the focus of the monograph. The reader learns
about powerful numerical methods for the solution ... context of derivative pricing.
The book does not claim to be a complete account of the state of the
art of the subject. Rather it attempts to provide a systematic framework for
an understanding of...
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Báo cáo hóa học: " Solving systems of nonlinear matrix equations involving Lipshitzian mappings" pdf
Ngày tải lên :
20/06/2014, 22:20
... Duan, F: Positive defined solution of two kinds of nonlinear matrix equations. Surv Math Appl. 4,
179–190 (2009)
12. Hasanov, V: Positive definite solutions of the matrix equations X ± A*X
-q
A ... for the
study of solutions to systems of nonlinear matrix equations involving contractive
mappings.
We first review the Thompson metric on the open convex cone P(n)(n ≥ 2), the set
of all nìn Hermitian ... solving
different classes of systems of nonlinear matrix equations involving Lipshitzian
mappings.
2000 Mathematics Subject Classifications: 15A24; 65H05.
Keywords: nonlinear matrix equations, Lipshitzian...
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Báo cáo hóa học: " Positive solutions for a coupled system of nonlinear differential equations of mixed fractional orders" pot
Ngày tải lên :
21/06/2014, 03:20
... Recently, there are a large number of papers dealing with the existence of
solutions of nonlinear fractional differential equations by the use of techniques of
nonlinear analysis (fixed point theore ... coupled system of nonlinear fractional differential equations. Appl Math Lett
2009,
22:64-69.
26. Gejji VD: Positive solutions of a system of nonlinear fractional differential equations. J Math ... Difference Equations 2011, 2011:10
http://www.advancesindifferenceequations.com/content/2011/1/10
Page 9 of 13
RESEARC H Open Access
Positive solutions for a coupled system of
nonlinear differential equations...
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