numerical solutions of nonlinear algebraic equations by secant bisection and newtonraphson methods
Numerical Solutions of the Black Scholes Equation
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25/10/2013, 19:20
... 8
Numerical Solutions of the Black
Scholes Equation
8.1 FINITE DIFFERENCE APPROXIMATIONS
(i) The object of this chapter is to explain various methods of solving the Black Scholes equation
by numerical ... the left-hand
edge of the grid (initial conditions) and the values at
the top and bottom edges (boundary conditions); the
solution of the problem is the series of values at the
right-hand edge. ... Solution of implicit method
i.e. we know u
i
M
and u
i
−M
. We can therefore calculate the right-hand side of equation (8.4)
since we also know the elements of the matrix B; this will be designated by...
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Tài liệu Solution of Linear Algebraic Equations part 1 docx
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... columns
of the matrix inverse of A (Đ2.1 and Đ2.3).
ã Calculation of the determinant of a square matrix A (Đ2.3).
If M<N,orifM=Nbut the equations are degenerate, then there are
effectively fewer 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 ... related by M equations. The
coefficients a
ij
with i =1,2, ,M and j =1,2, ,N are known numbers, as
are the right-hand side quantities b
i
, i =1,2, ,M.
Nonsingular versus Singular Sets of Equations
If...
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Tài liệu Solution of Linear Algebraic Equations part 2 ppt
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15/12/2013, 04:15
... J.H., and Reinsch, C. 1971,
Linear Algebra
,vol.IIof
Handbook for Automatic Com-
putation
(New York: Springer-Verlag).
Westlake, J.R. 1968,
A Handbook of Numerical Matrix Inversion and Solution of ... writeout equations
only for the case of four equations and four unknowns, and with three different right-
hand side vectors that are known in advance. You can write bigger matrices and
extend the equations ... 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...
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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 ... 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 ... the set of
n
linear equations A · x = b.
a[1 n][1 n]
,
c[1 n]
,and
d[1 n]
are
input as the output of the routine
qrdcmp
and are not modified.
b[1 n]
is input as the
right-hand side vector, and is...
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Tài liệu Solution of Linear Algebraic Equations part 3 pdf
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24/12/2013, 12:16
... 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 ... 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 ... reduced, and the increasing numbers of
predictable zeros reduce the count to one-third), and
1
2
N
2
M times, respectively.
Each backsubstitution of a right-hand side is
1
2
N
2
executions of a similar...
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Tài liệu Solution of Linear Algebraic Equations part 4 docx
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24/12/2013, 12:16
... 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 and the ... 1968,
A Handbook of Numerical Matrix Inversion and Solution of Linear Equations
(New York: Wiley).
2.3 LU Decomposition and Its Applications
Suppose we are able to write the matrix A as a product of ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 5 docx
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24/12/2013, 12:16
... l++;
}
}
The routines bandec and banbks are based on the Handbook routines bandet1 and
bansol1 in
[1]
.
CITED REFERENCES AND FURTHER READING:
Keller, H.B. 1968,
Numerical Methods for Two-Point ... 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 ... York:
McGraw-Hill),
Đ
9.11.
Horn, R.A., and Johnson, C.R. 1985,
Matrix Analysis
(Cambridge: Cambridge University Press).
2.4 Tridiagonal and Band Diagonal Systems
of Equations
The special case of a system of linear equations...
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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 (C) 1988-1992 by Cambridge University ... if the a’s and c’s are scalars, but as matrix inversion if the a’s and c’s are
themselves submatrices. Imagine doing the inversionof a very large matrix, of order
N =2
m
, recursively by partitions ... matrices
a
11
a
12
a
21
a
22
and
c
11
c
12
c
21
c
22
(2.11.5)
are 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
=...
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Tài liệu Solution of Linear Algebraic Equations part 6 pptx
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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 0-521-43108-5)
Copyright (C) 1988-1992 by Cambridge University ... n]
, and the vectors
b[1 n]
and
x[1 n]
are input, as is the dimension
n
.
Also input is
alud[1 n][1 n]
,theLU decomposition of
a
as returned by
ludcmp
,and
the vector
indx[1 n]
also returned by ... 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 (C) 1988-1992 by Cambridge University...
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Tài liệu Solution of Linear Algebraic Equations part 7 docx
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... 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 ... 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 2.6.1. ... 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...
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Tài liệu Solution of Linear Algebraic Equations part 8 docx
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... theWoodburyformula and successiveapplications of the Sherman-
Morrison formula is now clarified by noting that, ifU is thematrix formedby columnsoutofthe
P vectors u
1
, ,u
P
,andVis the matrix formed by columnsout ... 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 ... from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software....
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- solution of nonlinear algebraic equations pdf
- solution of nonlinear algebraic equations matlab
- solution of nonlinear algebraic equations
- numerical solutions of nonlinear algebraic equations by secant method
- existence of solution of nonlinear algebraic equations
- numerical solution of systems of nonlinear algebraic equations
- numerical solution of nonlinear algebraic equations by secant
- solution of nonlinear algebraic equations ppt
- numerical solutions of nonlinear algebraic equations by secant pdf
- solutions of nonlinear algebraic equations pdf
- numerical solution of linear algebraic equations
- numerical solutions of nonlinear algebraic equations by secant bisection
- discontinuous solutions of nonlinear differential equations
- solutions of partial differential equations by duffy pdf
- numerical solutions of ordinary differential equations
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