This paper introduces a design tool and its associated procedures for determining the sensitivity of outputs in a digital signal processing design to small errors introduced by rounding or truncation of internal variables. The proposed approach can be applied to both linear and nonlinear designs. By analyzing the resulting sensitivity values, the proposed procedure is able to determine an appro...

Abstract– Estimating the generalization capability is one of the most important problems in supervised learning. Therefore, various generalization error estimators have been proposed so far, in the presence of noise in output values. On the other hand, noise often exists in input values as well as output values. In this paper, we therefore investigate the influence of input noise on a generaliz...

The implementation of reliable and efficient geometric algorithms is a challenging task. The reason is the following conflict: On the one hand, computing with rounded arithmetic may question the reliability of programs while, on the other hand, computing with exact arithmetic may be too expensive and hence inefficient. One solution is the implementation of controlled perturbation algorithms whi...

Recent advances in network theory have led to considerable progress in our understanding of complex real world systems and their behavior in response to external threats or fluctuations. Much of this research has been invigorated by demonstration of the 'robust, yet fragile' nature of cellular and large-scale systems transcending biology, sociology, and ecology, through application of the netwo...

in this study a nonlinear asymmetric instability analysis carried out to study primary atomization of annular liquid sheets emanating from the prefilming airblast atomizer using a perturbation method and potential flow assumption. in this direction, firstly governing equations derived according to potential flow assumption and conservation equations while dynamic and static boundary condition a...

We present oneand two-loop results for the ghost propagator in Landau gauge calculated in Numerical Stochastic Perturbation Theory (NSPT). The one-loop results are compared with available standard Lattice Perturbation Theory in the infinite-volume limit. We discuss in detail how to perform the different necessary limits in the NSPT approach and discuss a recipe to treat logarithmic terms by int...

We study a scalar field in curved space in three dimensions. We compare the results obtained by using perturbation theory and numerical solutions, especially regarding to singularity behaviour at infinity. We find that both methods point to the necessity of excising the space-time around the origin. key words: black holes, Choptuik formation, + [email protected] * [email protected]

This paper is concerned with a relative perturbation theory and its entrywise relatively accurate numerical solutions of an M -matrix Sylvester equation AX + XB = C by which we mean both A and B have positive diagonal entries and nonpositive off-diagonal entries and P = Im⊗A+B⊗ In is a nonsingular M -matrix, and C is entrywise nonnegative. It is proved that small relative perturbations to the e...

We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range ...