Related papers: Solution Method For Higher Order System
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier…
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
We extend the nonlocal operator method to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original nonlocal operator method proposed by the authors in [A…
Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…
Weighted finite-state machines are a fundamental building block of NLP systems. They have withstood the test of time -- from their early use in noisy channel models in the 1990s up to modern-day neurally parameterized conditional random…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used…
Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
In this paper we present a novel method for the numerical solution of linear transport equations, which is based on ridgelets. Such equations arise for instance in radiative transfer or in phase contrast imaging. Due to the fact that…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based…
In recent years, much effort in designing numerical methods for the simulation and optimization of mechanical systems has been put into schemes which are structure preserving. One particular class are variational integrators which are…
We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…
In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a…
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler…