منابع مشابه
Evaluation of the Exponential Integral for Large Complex Arguments
has been prepared by th e National Bureau of Standards [1]; 1 th e introduction to the table gives a precise definition of this function. This table covers the range Ixl ~ 20, Iyl ~ 20, with argumcnts variously spaced. In order to compute E1( z) olltsid e this range, (or within this range, a t points where interpolation is awkward, which are those with comparatively large argument), several met...
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We study the large N limit of the Itzykson – Zuber integral and show that the leading term is given by the exponent of an action functional for the complex inviscid Burgers (Hopf) equation evaluated on its particular classical solution; the eigenvalue densities that enter in the IZ integral being the imaginary parts of the boundary values of this solution. We show how this result can be applied...
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Implementations of the heat balance integral method are discussed in which exponential functions are used in place of the familiar polynomial approximants. The rationale is based upon that of least-squares in that the use of ‘appropriate’ basis functions can enhance solution accuracy. Whilst this is true in principle it is shown that considerable skill must be exercised when deviating from poly...
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The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging to compute useful numerical bounds on the exponential decay rate. This work presents a generalization of the classical IQC results of Megretski and Rantzer [1...
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ژورنال
عنوان ژورنال: Journal of Research of the National Bureau of Standards
سال: 1959
ISSN: 0091-0635
DOI: 10.6028/jres.062.022