First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...

This paper presents a saddlepoint approximation to the cumulative distribution function of a random vector. The proposed approximation has accuracy comparable to that of existing expansions valid in ...

Particle methods are popular computational tools for Bayesian inference in nonlinear non-Gaussian state space models. For this class of models, we present two particle algorithms to compute the score ...

Nuclear physicists at the University of Washington developed a new framework to analyze how theoretical approximations influence quantum computers' representation of many-body systems required for ...

The number represented by pi (π) is used in calculations whenever something round (or nearly so) is involved, such as for circles, spheres, cylinders, cones and ellipses. Its value is necessary to ...

String theory began over 50 years ago as a way to understand the strong nuclear force. Since then, it’s grown to become a theory of everything, capable of explaining the nature of every particle, ...

Xiaojing Ye does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...

The FD= and FDHESSIAN= options specify the use of finite difference approximations of the derivatives. The FD= option specifies that all derivatives are approximated using function evaluations, and ...