Autonomous modal parameter estimations may involve sorting a large number of possible solutions to develop one consistent estimate of the modal parameters (frequency, damping, mode shape, and modal scaling). Once the final, consistent estimate of modal parameters is established, this estimate can be compared to related solutions from the larger set of solutions to develop statistical attributes...

We are interested in the rate of convergence of the Euler scheme approximation of the solution to a stochastic differential equation driven by a general (possibly discontinuous) semimartingale, and by the asymptotic behavior of the associated normalized error. It is well known that for Itô’s equations the rate is 1/ √ n ; we provide a necessary and sufficient condition for this rate to be 1/ √ ...

While properties of the weighted central path for linear and non-linear programs have been studied for years, the eeect that weighting the central path has on its limiting derivatives has not been fully explored. We show that when there is a unique dual solution, the limiting derivatives of the central path for a linear program are uniformly bounded over a set of normalized weights. Consequentl...

In our paper, we consider Tikhonov regularization in the reproducing Kernel Hilbert Spaces. In this space we derive upper and lower bound of the interval which contains the optimal value of Tikhonov regularization parameter with respect to the sensitivity of the solution without computing the singular values of the corresponding matrix. For the case of normalized kernel, we give an explicit for...