linear and nonlinear simultaneous equations calculator
SAP2000® Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures
Ngày tải lên :
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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SAP2000® Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures GETTING STARTED doc
Ngày tải lên :
01/04/2014, 03:20
... Dimensions and tolerances – merge, selection, and snap
tolerances; font sizes; zoom increment; and others
Design codes and their parameters
Colors of objects and results for display and printing ... Design,
Display, and Output operations.
To select, enable the Select Mode using the Draw menu > Set Select
Mode command, or by choosing any command from the Select menu.
Draw Mode and Select ... systems, end
offsets, insertion points, output locations, nonlinear properties,
line springs and masses, automated meshing parameters, and
more
Assigning properties to area objects, including...
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gerald beresford whitham linear and nonlinear waves pure and applied mathematics 1974
Ngày tải lên :
12/06/2014, 16:26
... by
nonlinear hyperbolic equations, and it has been used and refined in many
other fields.
In elasticity, the classical wave theory is also obtained after lineariza-
tion. Even with the linear ...
15.4 Nonlinear Group Velocity, Group Splitting, Shocks, 519
15.5 Higher Order Dispersive Effects, 522
15.6 Fourier Analysis and Nonlinear Interactions, 527
16 Applications of the Nonlinear ... explosions and the sonic booms of high speed aircraft. But
the whole intricate machinery of nonlinear hyperbolic equations had to be
developed for their prediction, and a full understanding required...
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Báo cáo hóa học: " Linear and Nonlinear Oblivious Data Hiding" ppt
Ngày tải lên :
23/06/2014, 01:20
... Newark, NJ, between March 2000 and August 2002. His re-
search interests include sensor/ad hoc networks, cryptography, data
hiding, and data compression.
Linear and Nonlinear Oblivious Data Hiding ... further studies establish that the
Linear and Nonlinear Oblivious Data Hiding 2103
part, a novel data hiding algorithm is proposed, and its per-
formance is analyzed and compared with existing schemes.
The ... Corporation
Linear and Nonlinear Oblivious Data Hiding
Litao Gang
InfoDesk, Inc., 660 White Plains Road, Tarrytown, NY 10591, USA
Email: lxg8906@njit.edu
Ali N. Akansu
Department of Electrical and Computer...
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david g luenberger yinyu ye linear and nonlinear programming international series in operati docx
Ngày tải lên :
27/06/2014, 17:20
... major parts: Linear Programming,
Unconstrained Problems, and Constrained Problems. The last two parts together
comprise the subject of nonlinear programming.
Linear Programming
Linear programming ... a standard linear program having n−1 variables and m−1
constraint equations. The value of the variable x
1
can be determined after solution
through (4).
30 Chapter 2 Basic Properties of Linear ... optimization structure—that character-
istic of linear and nonlinear programming. Examples of situations leading to this
structure are sprinkled throughout the book, and these examples should help to
indicate...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 1 doc
Ngày tải lên :
06/08/2014, 15:20
... PROPERTIES
OF LINEAR
PROGRAMS
2.1 INTRODUCTION
A linear program (LP) is an optimization problem in which the objective function
is linear in the unknowns and the constraints consist of linear equalities and ... major parts: Linear Programming,
Unconstrained Problems, and Constrained Problems. The last two parts together
comprise the subject of nonlinear programming.
Linear Programming
Linear programming ... Descent 233
Linear and Nonlinear
Programming
Third Edition
David G. Luenberger
Stanford University
Yinyu Ye
Stanford University
123
PART I
LINEAR
PROGRAMMING
1.4 Iterative Algorithms and Convergence...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 2 ppsx
Ngày tải lên :
06/08/2014, 15:20
... natural interpretation of (1) as a set of m equations.
If m<nand the equations are linearly independent, then there is not a unique
solution but a whole linear variety of solutions (see Appendix ... different
additional equations of this special form.
If the equations (3) are linearly independent, we may replace a given equation
by any nonzero multiple of itself plus any linear combination of the other equations
in ... Bazaraa,
Jarvis, and H. F. Sherali [B6], Bertsimas and Tsitsiklis [B13], Cottle, [C6], Dantzig and
Thapa [D9, D10], Nash and Sofer [N1], Saigal [S1], and Vanderbei [V3]
2.5 An excellent discussion of...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 3 ppsx
Ngày tải lên :
06/08/2014, 15:20
... efficiency and numerical stability, however, this pivoting
procedure is not as effective as the method of Gaussian elimination for general
systems of linear equations (see Appendix C), and it therefore ... initially, a last row consisting of the c
i
’s and a right-hand side of zero can be
appended to the standard array to represent this additional equation. Using standard
pivot operations, the elements ... types of linear programs, however,
and it is necessary to develop a means for determining one so that the simplex
method can be initiated. Interestingly (and fortunately), an auxiliary linear program
and...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 4 doc
Ngày tải lên :
06/08/2014, 15:20
... artificial basis
technique; Dantzig, Orden and Wolfe [D8], Orchard-Hays [O1], and Dantzig [D4] for the
revised simplex method; and Charnes and Lemke [C3] and Dantzig [D5] for upper bounds.
The synthetic ... several fixed origins and destinations so as
to minimize transportation cost while satisfying demand. Referring to (6) and (7)
of Chapter 2, the problem is in standard form, and hence the asymmetric ... 77
Delete all rows and columns that do not contain pivots during a cycle, obtaining a new
linear program that also cycles. Assume that this reduced linear program has m rows
and n columns. Consider...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 5 docx
Ngày tải lên :
06/08/2014, 15:20
... x
3
=0.
∗
4.7 REDUCTION OF LINEAR INEQUALITIES
Linear programming is in part the study of linear inequalities, and each progressive
stage of linear programming theory adds to our understanding of this important
fundamental ... 12
and x
i
0i=16
17. Given the linear programming problem in standard form (3) suppose a basis B and the
corresponding (not necessarily feasible) primal and dual basic solutions x and ... understanding of how the modern theory of linear
programming evolved, and help make clear how complexity theory impacts linear
programming. However, the reader may wish to consider them optional and...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 6 pptx
Ngày tải lên :
06/08/2014, 15:20
... chapters.
Not only have nonlinear methods improved linear programming, but interior-
point methods for linear programming have been extended to provide new
approaches to nonlinear programming. This ... intended to show how
this merger of linear and nonlinear programming produces elegant and effective
methods. These ideas take an especially pleasing form when applied to linear
programming. Study of ... x
3
and x
4
are slack variables for the original problem to put it in standard
form. The optimality conditions for x consist of the original 2 linear constraint
equations and the four equations
y
1
+s
1
=1
y
2
+s
2
=0
y
1
+s
3
=0
y
2
+s
4
=0
together...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 7 pps
Ngày tải lên :
06/08/2014, 15:20
... [T11], and others.
The homogeneous and self-dual embedding method can be found in Ye et al. [Y2], Luo
et al. [L18], Andersen and Ye [A5], and many others. It is also implemented in most linear
programming ... right
corner element, and it gives u
4
=2. Then, from the equation 4 =2 +
4
,
4
is found
to be 2. Next, u
3
and u
2
are determined, then
3
and
2
, and finally u
1
and
1
. The
result is ... Tanabe [T2] and Todd and Ye [T5]. The primal-dual potential reduction algorithm was
developed by Ye [Y1], Freund [F18], Kojima, Mizuno and Yoshise [K7], Goldfarb and
Xiao [G11], Gonzaga and Todd...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 8 pdf
Ngày tải lên :
06/08/2014, 15:20
... Transportation and Network Flow Problems
C =
⎡
⎢
⎢
⎢
⎢
⎣
03364
30548
35025
64205
48550
⎤
⎥
⎥
⎥
⎥
⎦
In this system points 1 and 2 are net suppliers, points 4 and 5 are net demanders, and
point 3 ... intermediate level,
and power is purchased directly only for peak demand periods. The requirements
are satisfied as shown in Fig. 7.2(b), where x
1
and x
2
denote the capacities of the
nuclear and coal-fired ... stone method.
6.5 The assignment problem has a long and interesting history. The important fact that the
integer problem is solved by a standard linear programming problem follows from a theorem
of...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 9 ppsx
Ngày tải lên :
06/08/2014, 15:20
... define corresponding
notions of average linear and average superlinear convergence.
Although the above array of definitions can be further embellished and
expanded, it is quite adequate for our purposes. ... r
k
k=0
and c
k
k=0
be sequences of real numbers. Suppose r
k
→0 average linearly
and that there are constants c>0 and C such that c c
k
C for all k. Show that
c
k
r
k
→0 average linearly.
14. ... 7.7.
Proposition. Let A X→Y and B Y →Z be point-to-set mappings. Suppose
A is closed at x and B is closed on A(x). Suppose also that if x
k
→ x and
7.4 Convex and Concave Functions 193
f
x
convex
(a)
f
x
nonconvex
(c)
f
x
convex
(b)
Fig....
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 10 pot
Ngày tải lên :
06/08/2014, 15:20
... −f
∗
Clearly 2a/A < 1 and hence there is linear convergence. Notice if that in fact is
chosen very close to .5 and is chosen very close to 1, then the stopping condition
demands that the be ... available,
fast convergence, and a guarantee of global convergence.
8.4 CLOSEDNESS OF LINE SEARCH
ALGORITHMS
Since searching along a line for a minimum point is a component part of most
nonlinear programming ... Exercise 2)
gx
k−1
x
k
= g
k
(14)
and
gx
k−1
x
k
x
∗
=
1
2
g
k (15)
where
k
and
k
are convex combinations of x
k
, x
k−1
and x
k
, x
k−1
, x
∗
, respec-
tively. Thus
x
k+1
−x
∗
=
g
k
2g
k
x
k
−x
∗
x
k−1
−x
∗
...
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