linear and nonlinear simultaneous equation solver

... 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....

Ngày tải lên: 06/09/2012, 15:56

... 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...

Ngày tải lên: 01/04/2014, 03:20

... 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 ... 473 13.14 Breaking and Peaking, 476 13.15 A Model for the Structure of Bores, 482 14 Nonlinear Dispersion and the Variational Method 485 14.1 A Nonlinear Klein-Gordon Equation, 486 14.2 ... 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...

Ngày tải lên: 12/06/2014, 16:26

... 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...

Ngày tải lên: 23/06/2014, 01:20

... 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...

Ngày tải lên: 27/06/2014, 17:20

... 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...

Ngày tải lên: 06/08/2014, 15:20

... 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 ... 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 ... 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...

Ngày tải lên: 06/08/2014, 15:20

... 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 ... 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 ... 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...

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...

Ngày tải lên: 06/08/2014, 15:20

... (25) represent a system of linear inequalities in standard form with one less variable and one less equation than the original system. The last equation is a simple linear equation from which x 1 is ... 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  0i=16 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...

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...

Ngày tải lên: 06/08/2014, 15:20

... 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 ... [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 ... 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...

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...

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....

Ngày tải lên: 06/08/2014, 15:20

... −f ∗  Clearly 2a/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 ... the logarithm of this equation we have, with y k =log M k , y k+1 =y k +y k−1  (18) which is the Fibonacci difference equation discussed in Section 7.1. A solution to this equation will satisfy y k+1 − 1 y k →0 Thus logM k+1 − 1 logM k →0 ... 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...

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20