Related papers: Improved Perturbation Method and its Application t…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
The increasing penetration of inertialess new renewable energy sources reduces the overall mechanical inertia available in power grids and accordingly raises a number of issues of grid stability over short to medium time scales. It has been…
We review recent developments in the type IIB matrix model, which was conjectured to be a nonperturbative formulation of superstring theory. In the first part we review the recent results for the Euclidean model, which suggest that SO(10)…
A new method of approximation scheme with potential application to a general interacting quantum system is presented. The method is non-perturbative, self- consistent, systematically improvable and uniformly applicable for arbitrary…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
In this paper, we establish a useful set of formulae for the $\sin\Theta$ distance between the original and the perturbed singular subspaces. These formulae explicitly show that how the perturbation of the original matrix propagates into…
We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations…
In this paper, higher-order perturbation theory is applied and tailored to one-dimensional ring-shaped Bose-Hubbard systems. Spectral and geometrical properties are used to structurally simplify the contributions and reduce computational…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
The perturbation technique within the framework of the asymptotic iteration method is used to obtain large-order shifted 1/N expansions, where N is the number of spatial dimensions. This method is contrary to the usual…
When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance…
We present a Maximum A Posteriori (MAP) derivation of the Independent Vector Analysis (IVA) algorithm, a blind source separation algorithm, by incorporating a prior over the demixing matrices, relying on a free-field model. In this way, the…
Late time cosmic acceleration may be achieved by modifying gravity on large scales. This should also have consequences on the evolution of perturbations. We thus extend our study of exponential infrared $f(T)$ teleparallel gravity to…
In this paper we consider filtering and smoothing of partially observed chaotic dynamical systems that are discretely observed, with an additive Gaussian noise in the observation. These models are found in a wide variety of real…
Perturbation theory is developed to analyze the impact of noise on data and has been an essential part of numerical analysis. Recently, it has played an important role in designing and analyzing matrix algorithms. One of the most useful…
We investigate in this paper an alternative method to simulation based recursive importance sampling procedure to estimate the optimal change of measure for Monte Carlo simulations. We propose an algorithm which combines (vector and…
We simulate the vibration of a violin bridge in a multi-query context using reduced basis techniques. The mathematical model is based on an eigenvalue problem for the orthotropic linear elasticity equation. In addition to the nine material…