相关论文: Least Squares Model Reduction: A Two-Stage System-…

Models of complex systems often consist of multiple interconnected subsystem/component models that are developed by multi-disciplinary teams of engineers or scientists. To ensure that such interconnected models can be applied for the…

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…

We develop a new least squares method for solving the second-order elliptic equations in non-divergence form. Two least-squares-type functionals are proposed for solving the equations in two steps. We first obtain a numerical approximation…

The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…

We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

We consider the linear least squares problem with linear equality constraints (LSE problem) formulated as $\min_{x\in\mathbb{R}^{n}}\|Ax-b\|_2 \ \mathrm{s.t.} \ Cx = d$. Although there are some classical methods available to solve this…

Model order reduction is the approximation of dynamical systems into equivalent systems with smaller order. Model reduction has been studied extensively for different types of systems. In this paper, we present two methods for multi input…

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential…

A method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points. This yields a robust and efficient method which can avoid singularities and breakdowns in the…

In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…

Adaptive cubic regularization methods for solving nonconvex problems need the efficient computation of the trial step, involving the minimization of a cubic model. We propose a new approach in which this model is minimized in a low…

In this paper we suggest a moment matching method for quadratic-bilinear dynamical systems. Most system-theoretic reduction methods for nonlinear systems rely on multivariate frequency representations. Our approach instead uses univariate…

Motivation: Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which…

We develop a model reduction technique for non-smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and non-smooth models on unions of slow and attracting spectral submanifolds…

Currently, the area of geometric modeling and the construction of 3D models based on point clouds from laser sensors is actively developing. One of the basic tasks of geometric modeling is the reconstruction of a surface from a cloud of…

An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…

We here characterize the minimality of realization of arbitrary linear time-invariant dynamical systems through (i) intersection of the spectra of the realization matrix and of the corresponding state submatrix and (ii) moving the poles by…

This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding…

A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the…