Ion mobility spectrometry (IMS) has been widely used for the on-site detection of trace chemicals, but continue to suffer from a low duty cycle ion injection. The Hadamard transform (HT-IMS) technique was employed address problem with increased signal-to-noise ratio (SNR). However, in this work, through simulation, certain deviation between mathematical principle and actual data collection proc...

This article makes use of simultaneous decomposition four quaternion matrixes to investigate some Sylvester-like matrix equation systems. We present useful necessary and sufficient conditions for the consistency system equations in terms equivalence form block matrixes. also derive general solution according partition coefficient As an application system, we practical a ϕ-Hermitian provide when...

In this paper, by extending the well-known Jacobi and Gauss–Seidel iterations for Ax = b, we study iterative solutions of matrix equations AXB = F and generalized Sylvester matrix equations AXB + CXD = F (including the Sylvester equation AX + XB = F as a special case), and present a gradient based and a least-squares based iterative algorithms for the solution. It is proved that the iterative s...

The problem of solving approximate GCD of multivariate polynomials has been well studied in the computational literature because of its importance particularly in engineering application[2, 6, 7]. Numbers of algorithms have been proposed to give the approach such as approximate subresultant PRS and modular algorithm using SVD. Here we focus on EZ-GCD[3], another method based on Hensel Lifting. ...

This paper addresses two problems: an image denoising problem assuming dense observations and an image reconstruction problem from sparse data. It shows that both problems can be solved by the Sylvester/Lyapunov algebraic equation. The Sylvester/Lyapunov equation has been extensively studied in Control Theory and it can be efficiently solved by well known numeric algorithms. This paper proposes...

The alternate Sylvester sums are Tm(a, b) = ∑ n∈NR(−1)n, where a and b are coprime, positive integers, and NR is the Frobenius set associated with a and b. In this note, we study the generating functions, recurrences and explicit expressions of the alternate Sylvester sums. It can be found that the results are closely related to the Bernoulli polynomials, the Euler polynomials, and the (alterna...

This paper deals with the design of a reduced-order H∞ filter for a stochastic bilinear system with a prescribed H∞ norm criterion. The considered system is bilinear in control and with multiplicative noises in the dynamics and in the measurement equations. The problem is transformed into the search of a unique gain matrix by using Sylvester-like constraints. The approach is based on the resolu...

In this paper, we propose two new algorithms based on modified global Arnoldi algorithm for solving large Sylvester matrix equations AX + XB = C where A ∈ Rn×n, B ∈ Rs×s, X and C ∈ Rn×s. These algorithms are based on the global FOM and GMRES algorithms and we call them by Global FOM-SylvesterLike(GFSL) and Global GMRES-Sylvester-Like(GGSL) algorithms, respectively. Some theoretical results and ...

Abstract Explicit expressions for restricted partition function W (s, d) and its quasiperiodic components W j (s, dm) (called Sylvester waves) for a set of positive integers dm = {d1, d2, . . . , dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli and Eulerian polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester ...

We provide necessary and sufficient conditions for the uniqueness of solution of the generalized Sylvester and ⋆-Sylvester equations, AXB − CXD = E and AXB+CX ⋆ D = E, respectively, where the matrix coefficients are allowed to be rectangular. These conditions generalize existing results for the same equations with square coefficients. Our characterization reveals unexpected constraints regardin...