L. W. Johnson and R. D. Riess, Numerical Analysis, Addison Wesley, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....plant behavior is learned by Model Learner. 2) When Model Learner provides a model of the current behavior, y 1 = OE(y 0 ; y 0 ; F c ) Controller determines the appropriate control input for a given initial state and a desired next position by solving this equation for F c using Newton s method [19]. In our experiments, we Plant Controller Model Learner Goal Reasoner Model Manager Local Model Database Fig. 4. Restructurable learning control architecture. terminate the iterations of Newton s method after an error smaller than 0:1 is achieved. Plant simulator accepts the controller input and ....

....control architecture. terminate the iterations of Newton s method after an error smaller than 0:1 is achieved. Plant simulator accepts the controller input and computes the plant s next state by integrating the system state equations, using the 4th order Runge Kutta algorithm with n = 10 steps [19]. Gaussian noise N(0; oe 2 ) with controlled variance oe 2 , can be added to the plant output. Various random events, like the breaking of the spring or the relocation of the liquid surface, can be read in from a setup file. Model Learner is responsible for learning the plant s local models ....

L. W. Johnson and R. D. Riess, Numerical Analysis, Addison Wesley, 1982.

....To perform 2D interpolation, we perform 1D interpolations in one dimension and then perform 1D interpolations on these results in the orthogonal dimension. In some situations, interpolating polynomials are not suitable because they exhibit an oscillatory behavior as their degree increases [16]. To overcome this oscillatory behavior and still provide a smooth interpolation, we use Cubic spline interpolation [34] Then Bicubic spline interpolation is performed as cubic spline interpolation first in one dimension and then cubic spline interpolation of those results in the orthogonal ....

L.W. Johnson and R.D. Riess. Numerical Analysis. Addison-Wesley, 1982.

....are slowly varying, the use of a larger time step should significantly reduce function evaluations. Figures (7a 7c) shows a particle trajectory computed for the tank illustrated in figure (5) from the point (0:85; 0:75; 0:0) on the inlet plane using the Fehlburg RK4(5) integrator (see for example [11]) Its coefficient tableau is given in table (5) Appendix A.1. Figure (7d) displays the time steps which were selected by the step control mechanism. Notice that the integration step of 5:06 Theta 10 Gamma6 , just after t = 18:7, was selected when the particle was passing through the plane z ....

L. W. Johnson and R. Dean Riess, 1982. Numerical Analysis. AddisonWesley.

.... solving the linear system Gamma Deltag = f(u) for g allows one to explicitly construct the array rJ(u) j u Gamma g, representing rJ(u) In order to solve this system, we used Gaussian Elimination for the ODE (N=1) and Gauss Sidel with successive overrelaxation (SOR, 1:73) for the PDE (see [9]) Remark 3.5 At one time this author projected Sobolev gradients rJ(u) onto tangent spaces T u S, thinking this necessary in order to keep iterates near the surface S. This turns out not to be necessary (although not particularly harmful) since projections of iterates u k onto S by P 1 or P ....

L. Johnson and R. Riess, Numerical Analysis, Reading, Mass.: Addison-Wesley (1982).

....such as the transaction length (i.e. number of pages read) or the write probability. CTCompTime, and SlackFactor a total of 208 combinations, or 832 simulations. This process was repeated for a number of threshold values in order to compute the optimal value per setting. The bisection method [17] was used in order to determine the optimal threshold value for each ArrivalRate, CTCompTime, SlackFactor triplet. To evaluate the relative performance of LAF, we ran a set of experiments in which LAF optimized the value of its threshold along all 3 dimensions using the results from the above ....

Lee W. Johnson and R. Dean Riess. Numerical Analysis. Addison Wesley, 1982.

....Y (t) does not exactly describe all the points y 1 ; y 2 ; y n . But the best (least amount of error) Y (t) is still desired. Numerous methods of minimum discrepancy exist to fit data to a linear function [1, 43] commonly known as the method of least squares) and more complex functions [33]. Periodic functions such as those necessary to model daily, weekly, and quarterly variations in workload on a computer system can be approximated accurately using fast Fourier transform techniques [33] Unfortunately, the mathematics is complicated and time consuming for techniques more advanced ....

.... function [1, 43] commonly known as the method of least squares) and more complex functions [33] Periodic functions such as those necessary to model daily, weekly, and quarterly variations in workload on a computer system can be approximated accurately using fast Fourier transform techniques [33]. Unfortunately, the mathematics is complicated and time consuming for techniques more advanced than least squares fit for a linear function. The network in which SPA operates has 100 200 hosts that are used by hundreds of users. There are dozens of supported programs on each of these hosts. To ....

Johnson, L. W., and Riess, R. D. Numerical Analysis. Addison-Wesley Publishing Company, Reading, MA, 1977.

.... = xH i (x) Gamma nH i Gamma1 (x) i = 2; 3; For a given order in the approximation, n, it is known that the interpolation at the roots of the polynomial H n 1 (x) will minimize the integrated squared approximation error with respect to the weight function exp( Gamma 1 2 x 2 ) see Johnson Riess (1982) and Abramowitz Stegun (1972) A polynomial of order n = 14 is found to be suitable. The pdf f( jc o ; s o ) is computed up to a multiplicative constant in the 15 roots of the Hermite polynomial H 15 ( Gamma oe ) with being the prior expectation of , ie 40; and oe being set to 3. This ....

Johnson, L. W. & Riess, R. D. (1982), Numerical Analysis, 2nd edn, Addison-Wesley, Reading, Massachusetts.

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