A relatively new branch of computational biology and chemistry has been emerging as an e ort to apply successful paradigms and algorithms from geometry and robot kinematics to predicting the structure of molecules, embedding them in Euclidean space, and nding the energetically favorable con gurations. We illustrate several e cient algebraic algorithms for enumerating all possible conformations ...

A direct method for eigenvalue reordering in a product of a K-periodic matrix sequence in periodic or extended periodic real Schur form is presented and analyzed. Each reordering of two adjacent sequences of diagonal blocks is performed tentatively to guarantee backward stability and involves solving a K-periodic Sylvester equation (PSE) and constructing a K-periodic sequence of orthogonal tran...

A direct method for eigenvalue reordering in a product of a K-periodic matrix sequence in periodic or extended periodic real Schur form is presented and analyzed. Each reordering of two adjacent sequences of diagonal blocks is performed tentatively to guarantee backward stability and involves solving a K-periodic Sylvester equation (PSE) and constructing a K-periodic sequence of orthogonal tran...

In this short note we deal with a constructive scheme to decompose a continuous family of matrices A(ρ) asymptotically as ρ → 0 into blocks corresponding to groups of eigenvalues of the limit matrix A(0). We also discuss the extension of the scheme to matrix families depending upon additional parameters and operators on Hilbert spaces. 1. Matrix theory 1.1. Preliminaries. We first recall some w...

General parametric solution to a family of generalized Sylvester matrix equations arising in linear system theory is presented by using the socalled generalized Sylvester mapping which has some elegant properties. The solution consists of some polynomial matrices satisfying certain conditions and a parametric matrix representing the degree of freedom in the solution. The results provide great c...

We derive a conjugate-gradient type algorithm to produce approximate least-squares (LS) solutions for an inconsistent generalized Sylvester-transpose matrix equation. The is always applicable any given initial and will arrive at LS solution within finite steps. When the equation has many solutions, can search one with minimal Frobenius-norm. Moreover, Y, find unique closest Y. Numerical experim...

Based on the higher-order restricted flows, first type of integrable deformed fourth-order matrix NLS equations, that is, equations with self-consistent sources (FMNLSSCS), is derived. By virtue $${\bar{\partial }}$$ -dressing method, second called NLS–Maxwell–Bloch system (FMNLS-MB) presented. We prove equivalence FMNLSSCS and FMNLS-MB successfully. Furthermore, N-soliton solutions are explici...

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...

We consider linear time-invariant (LTI) systems of the following form Σ : { ẋ(t) = Ax(t) + Bu(t), t > 0, x(0) = x, y(t) = Cx(t) + Du(t), t ≥ 0, with stable state matrix A ∈ Rn×n and B ∈ Rn×m, C ∈ Rp×n, D ∈ Rp×m, arising, e.g., from the discretization and linearization of parabolic PDEs. Typically, in practical applications, we have a large state-space dimension n = O(105) and a small input and ...

In recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. The following method is based on vector forms of Haar-wavelet functions. In this paper, we will introduce one dimensional Haar-wavelet functions and the Haar-wavelet operational matrices of the fractional order integration. Also the Haar-wavelet operational matrices of ...