| W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in Fortran: The Art of Scientific Computing (Cambridge University Press, 1996). |
....dwell times vector ) is to be optimized. The fitness function for this optimization is defined by the Euclidian distance between the computed resist profile associated to a scanned pattern and an target resist profile. To solve this optimization problem, a SD search algorithm was implemented [22] [23]. Because no a priori information on the topology of the search landscape was known, the SD algorithm was chosen because of the high dimensionality of the search space. Indeed, compared to, e.g. Powell algorithms [23] the SD algorithm should be less sensitive to the complexity of the search ....
....To solve this optimization problem, a SD search algorithm was implemented [22] 23] Because no a priori information on the topology of the search landscape was known, the SD algorithm was chosen because of the high dimensionality of the search space. Indeed, compared to, e.g. Powell algorithms [23], the SD algorithm should be less sensitive to the complexity of the search landscape because it is not necessary that a general direction point towards the global minimum. It should, therefore, be better suited for these kinds of problems. The SD method is based on successive transformations of ....
W. H. Press, Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. New York: Cambridge Univ. Press, 1992.
....summation orders on different number of processors. A slight change on the least significant bits will accumulate quickly into the significant bits in c,fi over several iterations, leading to a different CG trajectory in the multi dimensional space, and a slightly different solution (see, e.g. [11, 22]) Although the self correcting nature of the conjugate gradient method ensures that these different solutions on different number of processors are equally correct with regard to solving the linear equation, this inherent difference generating nature could be significant. It is feared that the ....
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in Fortran: the Art of Scientific Computing. 2nd Edition. Cambridge University Press, Cambridge, UK, 1992.
....general method For simplicity, we give an example of single threaded code with rectangular arrays. Section 9 will discuss the application of these optimizations to multithreaded code. The program of Figure 8 will be used in this example. It implements a step of a two dimensional Jacobi relaxation [6]. We chose it because it is a well known operation that illustrates a loop nest with various array references in its body. Also, the array references all use slightly different indices, making our example more interesting. Figure 9 shows the loop implemented with naive tests. The statement ....
....region without tests is divided again. This partitioning is illustrated in Figure 15, for a two dimensional iteration space. r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r R[1] R[2] R[5] R[8] R[11] R[3] R[6] R[9] R[12] R[4] R[7] R[10] R[13] R[14] l i 2 u i 2 ffl R[1] tests in i 1 and i 2 ffl R[2] R[5] R[8] R[11] tests in i 2 ffl R[3] R[6] R[9] R[12] no tests ffl R[14] tests in i 1 and i 2 (A) Partitioning the iteration space into regions (B) Mandatory tests in ....
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge University Press, 1992.
....by Matlab s Symbolic Math Toolbox [40] Notice that the off stopping criterion results in fewer iterations but provides less accurate computed singular values and a U completely lacking orthogonality. A bizarre stopping criterion for Jacobi s method for the symmetric eigenproblem is used in [46], based on testing whether off(A) underflows to zero. Proper choice of stopping criterion is vital if a reliable Jacobi code is to be produced. Convergence of the algorithm corresponds to A A being diagonal, which means that the columns of A are orthonormal with 2 norms equal to the singular ....
William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Second edition, Cambridge University Press, 1992. xxvi+963 pp. ISBN 0 521 43064 X.
....potential is calculated by (18) Analogous expressions exist for the other surfaces. To compute these expressions in an acceptable time, the Fourier transform is applied, which cuts the computation time down from the order to . With proper zero padding, the convolution theorem can be exploited [31]. For the example of the potential values in the interior (17) the following transforms are required (Fourier transformed quantities are marked by a tilde sign in the following, the convolution in real space is represented by the symbol ) FFT FFT FFT FFT (19) The Fourier transformed ....
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge: Cambridge Univ. Press, 1992.
....n A 1 A 2 . A n FullPath n 1 FullPath n 2 . FullPath n 3 As long as all of the x i s are distinct, the matrix is a Vandermonde matrix (and thus has full rank) and is solvable in n 2 field operations [17]. Assuming that we get a unique x j in each packet, we can recover a path of length d with only d packets. The downside, however, is that this scheme would require log 2 p log 2 d # bits per packet (the first term is the encoding of the running FullPath and the second term is ....
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge University Press, 1992.
....errors of the gyro at different rates of rotation and temperatures without any compensation. Finding an error model from the measurements, w g and T, is a two input single output system identification problem. In order to use a general least square algorithm, we adopted a Vandermonde matrix [9] that reduces the problem to a single input single output system. Figure 3b shows the errors of the gyro after correcting its output with the compensation function (see [3] for more details) 3. IMPLEMENTATION OF THE DEADRECKONING NAVIGATION SYSTEM To be useful, a dead reckoning navigation system ....
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. 1982, "Numerical Recipes in FORTRAN: The Art of Scientific Computing." 2nd ed. Cambridge, England: Cambridge Univ. Press, pp. 82-89.
....sequence is a distorted version of the infinite sequence s transform. In order to reduce this side lobe effect, we can use tapers that increase to unity and decrease to zero more gradually than the rectangular or box car taper. Some common tapers are those of Bartlett, Hann, Hamming, and Welch [11]. Decreasing the side lobe effect can be achieved only by broadening the taper s main lobe, i.e. by reducing the spectral resolution. Therefore, it is not always useful to apply a data taper to the series. On the one hand, when studying a spectrum that exhibits a large dynamic range, lowlevel ....
Press W.H., Flannery B.P., Teukolski S.A. and Vettering W.T., Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge Univ. Press, UK) 1992.
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W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in Fortran: The Art of Scientific Computing (Cambridge University Press, 1996).
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Press, W. H.; Teulosky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in FORTRAN: The Art of Scientific Computing; Cambridge University Press, Cambridge, UK., 1992.
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W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran: The Art of Scientific Computing (2nd Edn.), Cambridge University Press, Cambridge, 1992.
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Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992) Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition, Cambridge Univ. Press, pp. 684-686.
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Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition, Cambridge Univ. Press, 1992, pp. 684686.
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Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition, Cambridge Univ. Press, 1992, pp. 684-686.
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B.P. Flannery, Numerical Recipes in Fortran77: The Art of Scientific Computing (Cambridge University Press, Cambridge, MA, 1992).
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Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition, Cambridge University Press, Cambridge, U. K. (1992).
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: the art of scientific computing, New York, Cambridge University Press, pp. 34-40, 1992.
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Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992) Numerical Recipes in FORTRAN: The Art of Scientific Computing, Second Edition, Cambridge Univ. Press, pp. 684-686.
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W.H. Press, S.A. Teukolsky, W.T.Vetterling, and B.P. Flannery. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge Univ. Press, New York, 1992.
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W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P Flannery, Numerical recipes in Fortran: the art of scientific computing - 2nd ed., New York: Cambridge University Press, 1992.
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Press, W. H., Teukkolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes in Fortran: The Art of Scientific Computing, 2 nd Edition, Cambridge University Press, 1992.
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed., pp. 490-498, Cambridge Univ. Press, New York, 1992.
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed., Cambridge University Press, New York #1992#.
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed., pp. 490-498, Cambridge Univ. Press, New York, 1992.
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William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Second edition, Cambridge University Press, 1992. xxvi+963 pp. ISBN 0 521 43064 X.
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