Descriptor systems consisting of a large number of differential-algebraic equations (DAEs) usually arise from the discretization of partial differential-algebraic equations. This paper presents an efficient algorithm for solving the coupled Sylvester equation that arises in converting a system of linear DAEs to ordinary differential equations. A significant computational advantage is obtained b...

We consider the solution of the ?-Sylvester equation AX±X?B? = C, for ? = T,H and A,B,∈ Cm×n, and some related linear matrix equations (AXB? ± X? = C, AXB? ± CX?D? = E, AX ± X?A? = C, AX ± Y B = C, AXB ± CY D = E, AXA? ± BY B? = C and AXB ± (AXB)? = C). Solvability conditions and stable numerical methods are considered, in terms of the (generalized and periodic) Schur, QR and (generalized) sing...

We consider the numerical approximation to the solution of the matrix equation A1X+XA2 −Y C = 0 in the unknown matrices X, Y , under the constraint XB = 0, with A1, A2 of large dimensions. We propose a new formulation of the problem that entails the numerical solution of an unconstrained Sylvester equation. The spectral properties of the resulting coefficient matrices call for appropriately des...

We provide a formula for variational quasi-Newton updates with multiple weighted secant equations. The derivation of the formula leads to a Sylvester equation in the correction matrix. Examples are given.

We present our public-domain software for the following tasks in sparse (or toric) elimination theory, given a well-constrained polynomial system. First, C code for computing the mixed volume of the system. Second, Maple code for defining an overconstrained system and constructing a Sylvester-type matrix of its sparse resultant. Third, C code for a Sylvester-type matrix of the sparse resultant ...

We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...

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...

We try to arm Newton’s iteration for univariate polynomial factorization with greater convergence power by shifting to a larger basic system of multivariate constraints. The convolution equation is a natural means for a desired expansion of the basis for this iteration versus the classical univariate method, which is more vulnerable to foreign distractions from its convergence course. Compared ...

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building a new DRP scheme in the same time. keywords DRP schemes, Sylvester equation