相关论文: Effective Subdivision Algorithm for Isolating Zero…
A new low-order discretization scheme for the identity operator in the magnetic field integral equation (MFIE) is discussed. Its concept is derived from the weak-form representation of combined sources which are discretized with…
With the increased availability of condition monitoring data and the increased complexity of explicit system physics-based models, the application of data-driven approaches for fault detection and isolation has recently grown. While…
For multiple-input multiple-output (MIMO) spatial-multiplexing transmission, zero-forcing detection (ZF) is appealing because of its low complexity. Our recent MIMO ZF performance analysis for Rician--Rayleigh fading, which is relevant in…
The approximation of a multiple isolated root is a difficult problem. In fact the root can even be a repulsive root for a fixed point method like the Newton method. However there exists a huge literature on this topic but the answers given…
An arbitrary $m\times n$ Boolean matrix $M$ can be decomposed {\em exactly} as $M =U\circ V$, where $U$ (resp. $V$) is an $m\times k$ (resp. $k\times n$) Boolean matrix and $\circ$ denotes the Boolean matrix multiplication operator. We…
Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…
A wide range of symbolic analysis and optimization problems can be formalized using polyhedra. Sub-classes of polyhedra, also known as sub-polyhedral domains, are sought for their lower space and time complexity. We introduce the Strided…
Various numerical linear algebra problems can be formulated as evaluating bivariate function of matrices. The most notable examples are the Fr\'echet derivative along a direction, the evaluation of (univariate) functions of…
Minimum achievable complexity (MAC) for a maximum likelihood (ML) performance-achieving detection algorithm is derived. Using the derived MAC, we prove that the conventional sphere decoding (SD) algorithms suffer from an inherent weakness…
Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical…
Root separation bounds play an important role as a complexity measure in understanding the behaviour of various algorithms in computational algebra, e.g., root isolation algorithms. A classic result in the univariate setting is the…
Derivative-free Riemannian optimization (DFRO) aims to minimize an objective function using only function evaluations, under the constraint that the decision variables lie on a Riemannian manifold. The rapid increase in problem dimensions…
The present paper focuses on the construction of a set of submatrices of a circulant matrix such that it is a smaller set to verify that the circulant matrix is an MDS (maximum distance separable) one, comparing to the complete set of…
In this paper the author introduces a new domain decomposition method for the solution of discretised integral equation eigenvalue problems. The new domain decomposition method is motivated by the so-called automated multi-level…
In this paper we focus on efficient implementations of the Multivariate Decomposition Method (MDM) for approximating integrals of $\infty$-variate functions. Such $\infty$-variate integrals occur for example as expectations in uncertainty…
Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs…
We consider the problem of interpolating a sparse multivariate polynomial over a finite field, represented with a black box. Building on the algorithm of Ben-Or and Tiwari for interpolating polynomials over rings with characteristic zero,…
Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where…
A function $F:\mathbb{F}_{2}^{n}\to \mathbb{F}_{2}^{m}$ is called $k$th-order sum-free if the sum of its values over any $k$-dimensional affine subspace of $\mathbb{F}_2^n$ is non-zero. Carlet recently introduced this notion and constructed…
A new 1D search method is proposed for minimizing an arbitrary real valued function. The algorithm is a modification of the interval halving method which is based on dividing the interval of uncertainty by three points into four equal…