Related papers: Balanced Truncation via Tangential Interpolation
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…
Model order reduction (MOR) is essential in integrated circuit design, particularly when dealing with large-scale electromagnetic models extracted from complex designs. The numerous passive elements introduced in these models pose…
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
In the analysis of Markov chains and processes, it is sometimes convenient to replace an unbounded state space with a "truncated" bounded state space. When such a replacement is made, one often wants to know whether the equilibrium behavior…
We describe a new method to compute general cubature formulae. The problem is initially transformed into the computation of truncated Hankel operators with flat extensions. We then analyse the algebraic properties associated to flat…
In this paper, we propose to combine imitation and reinforcement learning via the idea of reward shaping using an oracle. We study the effectiveness of the near-optimal cost-to-go oracle on the planning horizon and demonstrate that the…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine…
The Fredholm integral equations of the first kind are a classical example of ill-posed problem in the sense of Hadamard. If the integral operator is self-adjoint and admits a set of eigenfunctions, then a formal solution can be written in…
In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…
The Harmonic Balance method provides a heuristic approach for finding truncated Fourier series as an approximation to the periodic solutions of ordinary differential equations. Another natural way for obtaining these type of approximations…
It was recently shown [7, 9] that "properly built" linear and polyhedral estimates nearly attain minimax accuracy bounds in the problem of recovery of unknown signal from noisy observations of linear images of the signal when the signal set…
This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function…
We show via examples that, when solving optimal control problems, representing the optimal state and input trajectory directly using interpolation schemes may not be the best choice. Due to the lack of considerations for solution…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A…
In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on…
The low multilinear rank approximation, also known as the truncated Tucker decomposition, has been extensively utilized in many applications that involve higher-order tensors. Popular methods for low multilinear rank approximation usually…