81,815 research outputs found
Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues
The Erlangian approximation of Markovian fluid queues leads to the problem of
computing the matrix exponential of a subgenerator having a block-triangular,
block-Toeplitz structure. To this end, we propose some algorithms which exploit
the Toeplitz structure and the properties of generators. Such algorithms allow
to compute the exponential of very large matrices, which would otherwise be
untreatable with standard methods. We also prove interesting decay properties
of the exponential of a generator having a block-triangular, block-Toeplitz
structure
A probabilistic algorithm to test local algebraic observability in polynomial time
The following questions are often encountered in system and control theory.
Given an algebraic model of a physical process, which variables can be, in
theory, deduced from the input-output behavior of an experiment? How many of
the remaining variables should we assume to be known in order to determine all
the others? These questions are parts of the \emph{local algebraic
observability} problem which is concerned with the existence of a non trivial
Lie subalgebra of the symmetries of the model letting the inputs and the
outputs invariant. We present a \emph{probabilistic seminumerical} algorithm
that proposes a solution to this problem in \emph{polynomial time}. A bound for
the necessary number of arithmetic operations on the rational field is
presented. This bound is polynomial in the \emph{complexity of evaluation} of
the model and in the number of variables. Furthermore, we show that the
\emph{size} of the integers involved in the computations is polynomial in the
number of variables and in the degree of the differential system. Last, we
estimate the probability of success of our algorithm and we present some
benchmarks from our Maple implementation.Comment: 26 pages. A Maple implementation is availabl
Rapid computation of L-functions for modular forms
Let be a fixed (holomorphic or Maass) modular cusp form, with
-function . We describe an algorithm that computes the value
to any specified precision in time
The devil is in the detail: hints for practical optimisation
Finding the minimum of an objective function, such as a least squares or negative log-likelihood function, with respect to the unknown model parameters is a problem often encountered in econometrics. Consequently, students of econometrics and applied econometricians are usually well-grounded in the broad differences between the numerical procedures employed to solve these problems. Often, however, relatively little time is given to understanding the practical subtleties of implementing these schemes when faced with illbehaved problems. This paper addresses some of the details involved in practical optimisation, such as dealing with constraints on the parameters, specifying starting values, termination criteria and analytical gradients, and illustrates some of the general ideas with several instructive examples
Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
In this paper, I propose a technique for recovering quantum dynamical
information from imaginary-time data via the resolution of a one-dimensional
Hamburger moment problem. It is shown that the quantum autocorrelation
functions are uniquely determined by and can be reconstructed from their
sequence of derivatives at origin. A general class of reconstruction algorithms
is then identified, according to Theorem 3. The technique is advocated as
especially effective for a certain class of quantum problems in continuum
space, for which only a few moments are necessary. For such problems, it is
argued that the derivatives at origin can be evaluated by Monte Carlo
simulations via estimators of finite variances in the limit of an infinite
number of path variables. Finally, a maximum entropy inversion algorithm for
the Hamburger moment problem is utilized to compute the quantum rate of
reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.
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