linear and nonlinear operators
SAP2000® Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures
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06/09/2012, 15:56
... EFFORT AND EXPENSE HAVE GONE INTO THE
DEVELOPMENT AND DOCUMENTATION OF SAP2000. THE PROGRAM HAS
BEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRAM,
HOWEVER, THE USER ACCEPTS AND UNDERSTANDS ...
spacing in the X, Y and Z direction. Set the number of grid spaces to
10 for the X direction, and to 1 for the Y and Z directions. Type 6 ft
into the X direction spacing edit box and press the Enter ...
Subdivide command to bring up the form in Figure 13. Select the
Auto Subdivide Frame option and check the at Intermediate Joints
and at Intersection with Other Frames check boxes, and click OK....
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Doctor of Philosophy in Mathematics Linear and Non-linear Operators, and The Distribution of Zeros of Entire Functions
Ngày tải lên :
10/03/2014, 16:15
... and π
n
(Ω), n ∈ N.
Problem 97. Characterize all linear operators T : π(Ω) → π(Ω) ∪ {0}.
Problem 98. Characterize all linear operators T : π
n
(Ω) → π(Ω) ∪{0} for n ∈ N.
J. Borcea and P. Br and en ... sequences are diagonal. Other linear operators which preserve hyperbolicity are not
as simple to describe. In 2007, J. Borcea and P. Br and en characterized all linear operators that
preserve hyperbolicity.
Theorem ... completely solved Problems 97 and 98 for all closed circular domains
and their boundaries, and in [9], they obtained multivariate extensions for all finite order linear
differential operators with polynomial...
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Root Finding and Nonlinear Sets of Equations part 1
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07/11/2013, 19:15
... Finding and
Nonlinear Sets of Equations
9.0 Introduction
We now consider that most basic of tasks, solving equations numerically. While
most equations are born with both a right-hand side and a ... 7, and 14.
Ralston, A., and Rabinowitz, P. 1978,
A First Course in Numerical Analysis
, 2nd ed. (New York:
McGraw-Hill), Chapter 8.
Householder, A.S. 1970,
The Numerical Treatment of a Single Nonlinear ... Numerical Treatment of a Single Nonlinear Equation
(New York:
McGraw-Hill).
9.1 Bracketing and Bisection
We will say that a root is bracketed in the interval (a, b) if f(a) and f(b)
have opposite signs....
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Tài liệu Declaring Increment and Decrement Operators pptx
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15/12/2013, 00:15
... own version of the increment (++) and decrement (––)
operators. The usual rules apply when declaring these operators; they must be public,
they must be static, and they must be unary. Here is ... value;
}
The increment and decrement operators are unique in that they can be used in prefix and
postfix forms. C# cleverly uses the same single operator for both the prefix and postfix
versions. ... memory use
and garbage collection overhead. Therefore, it is recommended that you limit operator
overloads when you define classes.
Declaring Increment and Decrement Operators
C#...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 2 docx
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... 352
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... *x2)
Given a function
func
and an initial guessed range
x1
to
x2
, the routine expands the range
geometrically until a root is bracketed by the returned values
x1
and
x2
(in which case
zbrac
returns
1
) ... it is said toconverge linearly. Methods
that converge as a higher power,
n+1
= constant × (
n
)
m
m>1(9.1.4)
are said to converge superlinearly. In other contexts linear convergence would...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 3 pptx
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... 354
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... guaranteed to converge: Local behavior might send it off
towards infinity.
356
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... REFERENCES AND FURTHER READING:
Ralston, A., and Rabinowitz, P. 1978,
A First Course in Numerical Analysis
, 2nd ed. (New York:
McGraw-Hill),
§
8.3.
Ostrowski, A.M. 1966,
Solutions of Equations and...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 4 doc
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15/12/2013, 04:15
... can
sometimes be fooled. Is there a way to combine superlinear convergence with the
sureness of bisection?
360
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES ... REFERENCES AND FURTHER READING:
Ralston, A., and Rabinowitz, P. 1978,
A First Course in Numerical Analysis
, 2nd ed. (New York:
McGraw-Hill),
§
8.3.
Ostrowski, A.M. 1966,
Solutions of Equations and ... 362
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 5 doc
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15/12/2013, 04:15
... York:
McGraw-Hill),
§
8.4.
Ortega, J., and Rheinboldt, W. 1970,
Iterative Solution of Nonlinear Equations in Several Vari-
ables
(New York: Academic Press).
Mandelbrot, B.B. 1983,
The Fractal Geometry ... criterion.
(*funcd)(rts,&f,&df);
The one new function evaluation per iteration.
368
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... 366
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 6 docx
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15/12/2013, 04:15
... linear remainder
P (x)=(x
2
+Bx + C)Q(x)+Rx + S. (9.5.15)
Given B and C, R and S can be readily found, by polynomial division (§5.3). We can
consider R and S to be adjustable functions of B and ... Consequently, the roots can become more and
more inaccurate. It matters a lot whether the inaccuracy creeps in stably (plus or
378
Chapter 9. Root Finding and Nonlinear Sets of Equations
Sample page ... degree
m
and the coefficients
a[0 m]
. The method is to construct an upper Hessenberg matrix whose
eigenvalues are the desired roots, and then use the routines
balanc
and
hqr
. The real and
imaginary...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 7 doc
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... Globally Convergent Methods for Nonlinear
Systems of Equations
We have seen that Newton’s method for solving nonlinear equations has an
unfortunate tendency to wander off into the wild blue yonder ... A.M. 1966,
Solutions of Equations and Systems of Equations
, 2nd ed. (New York:
Academic Press).
Ortega, J., and Rheinboldt, W. 1970,
Iterative Solution of Nonlinear Equations in Several Vari-
ables
(New ... vector of values x
i
and F denote the entire vector of
functions F
i
. In the neighborhood of x, each of the functions F
i
can be expanded
9.6 Newton-Raphson Method for Nonlinear Systems of Equations
379
Sample...
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Tài liệu Root Finding and Nonlinear Sets of Equations part 8 ppt
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15/12/2013, 04:15
... Globally Convergent Methods for Nonlinear
Systems of Equations
We have seen that Newton’s method for solving nonlinear equations has an
unfortunate tendency to wander off into the wild blue yonder ... A.M. 1966,
Solutions of Equations and Systems of Equations
, 2nd ed. (New York:
Academic Press).
Ortega, J., and Rheinboldt, W. 1970,
Iterative Solution of Nonlinear Equations in Several Vari-
ables
(New ... (i=1;i<=n;i++) xold[i]=x[i]; Store x,
fold=f; and f .
for (i=1;i<=n;i++) p[i] = -fvec[i]; Right-hand side for linear equations.
ludcmp(fjac,n,indx,&d); Solve linear equations by LU decompo-
sition.lubksb(fjac,n,indx,p);
lnsrch(n,xold,fold,g,p,x,&f,stpmax,check,fmin);
lnsrch...
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Tài liệu Bài 12: ICA by Nonlinear Decorrelation and Nonlinear PCA doc
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23/12/2013, 07:19
... still a linear subspace. Only the coefficients corresponding
to the principal components are nonlinear functions of
x
. It should be noted that
254
ICA BY NONLINEAR DECORRELATION AND NONLINEAR ... tells us what
kind of nonlinearities should be used, as discussed in Chapter 9.
240
ICA BY NONLINEAR DECORRELATION AND NONLINEAR PCA
is a stochastic gradient algorithm and the other one a recursive ... (Electronic)
260
ICA BY NONLINEAR DECORRELATION AND NONLINEAR PCA
W1 W2 −W3
−W4 W5 W6
−W7 −W8 −W9
Fig. 12.5
The whitened images.
vector,
y(t)
is the output vector,
W(t)
is the weight matrix, and
g
is the nonlinearity
in...
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