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The numerical errors in inverse simulation
Flight Simulation and Technologies, 1993This paper analyzes the numerical errors of two categories of inverse simulation algorithms: differentiation inverse method and integration inverse method. A fist-order differential equation is used to demonstrate the concept. The results of the inverse simulation are used as step-function inputs to the differential equation for a forward simulation ...
Lin, K. C., Lu, P., Smith, M.
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Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms
INFORMS Journal on Computing, 1997It is known that probability density functions and probability mass functions usually can be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions, respectively) with the Fourier-series method. Other more general functions can be substantially more difficult to invert, because the aliasing and ...
Gagan L. Choudhury, Ward Whitt
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A Numerical Method for the Inverse Stochastic Spectrum Problem
SIAM Journal on Matrix Analysis and Applications, 1998This paper concerns the construction of a stochastic matrix with a prescribed spectrum. The present ``flow approach'' is based on a differential equation to obtain the steepest descent flow for reducing the distance (given, say, in terms of the Frobenius norm) between isospectral matrices and nonnegative matrices.
Moody T. Chu, Quanlin Guo
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Numerical inversions of characteristic functions
Scandinavian Actuarial Journal, 1975abstract This paper contains a comparison between different methods to evaluate numerically the integral leading from the characteristic function to the corresponding probability distribution function.
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Numerical inversion of Laplace transform
Calcolo, 1967The paper describes a general method for the numerical calculation of Laplace's inverse transform of a given function. The general method is then specialized to two cases in which the computer is shown to be of great use. An appendix contains the solution of the collateral problem of the numerical derivation of a function.
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Numerical Inversion of the Mellin Transform
IMA Journal of Applied Mathematics, 1977Theocaris, P. S., Chrysakis, A. C.
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Numerical analysis of inverse problems
Journal of Inverse and Ill-Posed Problems, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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NUMERICAL TRANSFORM INVERSION FOR AUTOCORRELATIONS OF WAITING TIMES
2005The generating function of the autocorrelations of successive waiting times in a stationary M/G/l or in a stationary GI/M/1 system can be expressed in terms of the probability generating function of the number of customers served in a busy period. The latter function is only implicitly determined as a solution to a functional equation.
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On the numerical inversion of the Laplace transform
Bulletin of the Seismological Society of America, 1964abstract Methods are demonstrated for the numerical calculation of the inverse Laplace transform g(t) of a function g(p) given on the positive real axis of the p-plane.
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Numerical Inversion of the Laplace Transform
1981We wish to present a practical way to numerically reconstruct G(r) from the experimentally measured correlation function g(x), i.e. deal with polydispersity problems: $$g\left( tau \right) = \int_o^\infty {G\left( T \right)} {e^{ - \Gamma \tau }}dT$$ (1)
Didier Sornette, Nicole Ostrowsky
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