numerical solution of simultaneous linear algebraic equations
Tài liệu Solution of Linear Algebraic Equations part 1 docx
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... 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 ... “pointer to array of pointersto rows.” You might wish to review that section
34
Chapter 2. Solution of Linear Algebraic Equations
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
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... 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 ... Springer-Verlag).
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York: Wiley).
Johnson, L.W., and Riess, R.D. 1982,
Numerical Analysis
, 2nd ed. (Reading, ... 36
Chapter 2. Solution of Linear Algebraic Equations
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Tài liệu Solution of Linear Algebraic Equations part 11 ppt
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... 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 RECIPES ... 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 ... purposes,
because of its greater diagnostic capability in pathological cases.)
Updating a QR decomposition
Some numericalalgorithms involve solvinga successionof linear systems each of which
differs...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
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... 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 ... 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 Analysis
, 2nd ed. ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
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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 ... 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 RECIPES ... (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
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Tài liệu Solution of Linear Algebraic Equations part 12 pdf
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... 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 ... (C) 1988-1992 by Numerical Recipes Software.
Permission is granted for internet users to make one paper copy for their own personal use. Further reproduction, or any copying of machine-
readable ... 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...
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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 ... 56
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 7 docx
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... 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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... 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 ... 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 ... before
sending it to the matrix multiply routine.
86
Chapter 2. Solution of Linear Algebraic Equations
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Tài liệu Solution of Linear Algebraic Equations part 9 docx
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... 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 ... 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 = i +1,i+2, ,N (2.9.5)
92
Chapter 2. Solution of Linear Algebraic Equations
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Tài liệu Numerical Solution of Stochastic Differential Equations with Jumps in Finance pdf
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... 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
∈ ... a small class of jump diffusion SDEs admits explicit solutions,
it is important to construct discrete-time approximations. The focus of this
monograph is the numerical solution of SDEs with jumps ... hardware devices and seems to provide
solutions where no alternative is known.
The focus of this book is on the numerical solution of stochastic differential
equations (SDEs) with jumps via simulation...
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